CHAPTER 14
FIVE PRACTICE PSATs
WITH DETAILED ANSWER
KEYS
3
X W
X W
X W
X W
X W
X W
X W
X W
X W
X W
X W
X W
X W
X
W
341
PRACTICE PSAT 1
343
CHAPTER 14 / PRACTICE PSAT 1
345
ANSWER SHEET
Last Name: ______________________________________
First Name: ____________________________________
Date: ___________________________________________
Testing Location:________________________________
Administering the Test
•
•
•
•
•
•
•
•
Remove this answer sheet from the book and use it to record your answers to this test.
This test will require 2 hours and 10 minutes to complete. Take this test in one sitting.
Use a stopwatch to time yourself on each section. The time limit for each section is written clearly at the
beginning of each section. The first four sections are 25 minutes long, and the last section is 30 minutes long.
Each response must completely fill the oval. Erase all stray marks completely, or they may be interpreted as responses.
You must stop ALL work on a section when time is called.
If you finish a section before the time has elapsed, check your work on that section. You may NOT move on
to the next section until time is called.
Do not waste time on questions that seem too difficult for you.
Use the test book for scratchwork, but you will only receive credit for answers that are marked on the
answer sheets.
Scoring the Test
•
•
•
•
Your scaled score, which will be determined from a conversion table, is based on your raw score for each
section.
You will receive one point toward your raw score for every correct answer.
You will receive no points toward your raw score for an omitted question.
For each wrong answer on a multiple-choice question, your raw score will be reduced by 1/4 point. For each
wrong answer on a numerical “grid-in” question (Section 4, questions 29–38), your raw score will receive no
deduction.
346
MC GRAW-HILL’S PSAT/NMSQT
CHAPTER 14 / PRACTICE PSAT 1
347
Section I
Æ
z
Time—25 minutes
1
24 Questions (1 –24)
Each of the sentences below is missing one or two portions. Read each sentence. Then select the choice
that most logically completes the sentence, taking into account the meaning of the sentence as a whole.
Example:
Rather than accepting the theory unquestioningly, Deborah regarded it with - - - - - - .
(A)
(B)
(C)
(D)
(E)
mirth
sadness
responsibility
ignorance
skepticism
Correct response: (E)
B
1
The seemingly offhand remark was in fact
part of a - - - - - - effort by the director to
make the actors feel that their jobs were at
risk.
(A)
(B)
(C)
(D)
(E)
B
2
B
3
embodiment
acquisition
vocation
corollary
acceptance
Although history has shown that the value of
our liberty is timeless, our appreciation of
such national - - - - - - seems all too often
------.
(A)
(B)
(C)
(D)
(E)
B
5
B
6
benevolence . . solid
virtues . . fleeting
concepts . . permanent
anachronisms . . transitory
diversions . . ephemeral
Jill Ker Conway’s autobiography explores the
- - - - - - of childhood, the unexpected changes
that occur in a young life.
(A)
(B)
(C)
(D)
(E)
parasitism . . helpful
cooperation . . itemized
mortality . . precarious
antagonism . . resourceful
symbiosis . . beneficial
Danitra knew at an early age that dancing
was her - - - - - -; it was what she was meant
to do, and she pursued it with singleminded commitment.
(A)
(B)
(C)
(D)
(E)
4
celebrated
calculated
required
reflexive
conventional
In true - - - - - - , two different animal species
develop a mutually - - - - - - relationship in
the same habitat.
(A)
(B)
(C)
(D)
(E)
B
vicissitudes
veneers
evanescence
vulnerabilities
attachments
Many scientists believe that an ancient
supernova may have - - - - - - human evolution
by bombarding the Earth with cosmic rays
that altered the global climate, thereby
- - - - - - our ancestors to climb down from
the trees and walk upright.
(A)
(B)
(C)
(D)
(E)
hastened . . pursuing
resolved . . forcing
terminated . . daring
spurred . . impelling
propelled . . defying
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348
MC GRAW-HILL’S PSAT/NMSQT
B
7
Æ
z1
When the Senator decided to - - - - - - his political party and affiliate himself with the opposition, he was understandably treated as
- - - - - - by those former colleagues whom he
had left behind.
(A)
(B)
(C)
(D)
(E)
B
8
repudiate . . a curator
abandon . . a recluse
ascertain . . a champion
complement . . an expatriate
forsake . . an apostate
Despite the many attempts at - - - - - -, the dictator could not be assuaged, and the bellicose
nature of his public announcements made it
clear that conflict could not be - - - - - -.
(A)
(B)
(C)
(D)
(E)
diplomacy . . disclosed
conciliation . . averted
tact . . denigrated
belligerence . . forestalled
jingoism . . circumvented
The passages below are followed by questions
based on their content and the relationship
between the passages. Answer each question
based on what is stated or implied in the
passages.
20
Passage 2
25
30
35
40
45
Questions 9–12 are based on the
following passages.
Passage 1
Line
5
10
15
I have given in to the practice, adopted long
ago by many of my colleagues, known as the
“beginning-of-the-year review,” even though
it abrades the very fiber of my being. It is,
fundamentally, an admission of failure.
Imagine the manager of a professional baseball
team spending the first few weeks of spring
training reviewing the names of the positions or
in what direction to run the bases. Yet the
students coming to us from the best high
schools in America need to be reminded of the
most fundamental academic tasks and tools—
forming hypotheses, adding fractions,
constructing a clear sentence. I can’t say with
great certainty what is happening in our high
schools, but I can say that glittering grades do
not always indicate glittering minds. There
seems to be no grounding, no sense of the
# 2004 Christopher Black and College Hill Coaching. Published by
permission of the author.
fundamental reasoning skills and concepts of
academia. I often wonder if our high schools
shouldn’t be spending more time making sure
their ladders are on secure footing before
sending so many students scrambling up.
B
9
B
10
In every choreographed educational crisis,
the “back to basics” line always kicks up its
heels the highest. The thinking is seemingly
irrefutable: our children won’t succeed without
a solid foundation in basic skills. They can’t do
calculus before they learn long division. They
can’t write a good college essay before they
learn the five-paragraph model. They can’t read
Shakespeare before learning the phonetic code.
The model is the pyramid: we must build a solid
foundation if our children are ever to reach
the pinnacle of education, where the most
profound questions of our era are examined.
But we are losing too many students in building
the pyramid. It is worth the risk to take them to
the top of the pyramid, unfinished as it may be,
so that they might see the glorious expanse of
knowledge before them, yet to be reached. If we
don’t take the time to show them that expanse,
they will likely never learn that their hard labor
has any real purpose. We are too worried about
failure, about not getting the right answers, that
our questions and our tasks have lost almost all
of their meaning.
Passage 1 is written from the perspective of
(A)
(B)
(C)
(D)
(E)
a
a
a
a
a
politician
college professor
high school teacher
high school student
parent
In Passage 2, the “top of the pyramid” (line
39) represents the point at which students
(A)
(B)
(C)
(D)
have mastered all of the basic skills
have been accepted into college
have acquired a degree
can glimpse the most challenging academic problems
(E) can outperform other students on standardized tests
GO ON TO THE NEXT PAGE Å Å Å
The two authors differ in their perspectives
on fundamental academic skills in that the
author of Passage 1 believes that
(A) they should not be taught, while the
author of Passage 2 believes that they
form the foundation of a good education
(B) they should be taught in high school,
while the author of Passage 2 believes
that they should be taught in college
(C) they are underemphasized in high
school, while the author of Passage 2
believes that they are overemphasized
(D) they can be mastered by all students,
while the author of Passage 2 believes
that they are beyond the ability of some
students
(E) they are inimical to higher education,
while the author of Passage 2 believes
that they should be the focus of a
college education
B
12
10
15
20
25
30
Which of the following devices is used by
BOTH authors?
(A)
(B)
(C)
(D)
(E)
statistics
vignette
hyperbole
personification
metaphor
The questions below are to be answered on the
basis of what is stated or implied in the
passage below or the introductory material
that precedes the passage.
Questions 13–24 are based on the
following passages.
35
40
45
50
The following passages examine the work of F. Scott
Fitzgerald, the American twentieth-century novelist.
Passage 1
Line
5
Regarding most of the criticism and much
of Fitzgerald’s work, I am once again struck by
the urge to respond to Fitzgerald’s writing.
Sometimes—often—that response is only an
exclamation of delight. Other times it is a need
to try to write out a response in one’s own
words. This is no time, at the end of a brief
introduction, to be starting an essay on
Fitzgerald. What follows are some jottings
55
60
occasioned by this encounter with Fitzgerald
and his critics.
First, modern criticism (certainly not of
Fitzgerald alone) is often too refined. The big
things having been said, young critics tend
to make too much of small things. Color
symbolism, the guest list in The Great Gatsby,
and the “gat” in “Gatsby” are examples of what
one hopes will not dominate criticism of
Fitzgerald’s work in the future.
Second, there is joy in Fitzgerald’s work that
should not be passed over in dwelling upon
profundities, complexities, and tragic
implications. Edmund Wilson described it early
as a “quality exceedingly rare among even the
young American writers of the day; he is almost
the only one among them who has any real
light-hearted gaiety.” Recognizing that quality
and acknowledging its worth may draw
attention to the variety to be found in a writer
who is commonly charged with having too
narrow a range. It also adds to the dimensions
of The Great Gatsby and Tender is the Night,
those novels that do most to maintain
Fitzgerald’s reputation as a serious writer.
For it is not only theme and technique that
distinguish these novels, but the flashes of
brilliance, comic as well as tragic, that
illuminate individual scenes.
Third, Fitzgerald’s style, as has been said
over and over, is his great strength. Here
scholarship has done a great service to
Fitzgerald. One’s awareness of his style is
enhanced by examining the manuscripts
through which the finished phrases and
paragraphs came into existence. One feels
better about one’s own strikeovers, and
pencillings, and second and third thoughts.
One learns.
Fourth, in the presence of so much
Fitzgerald scholarship, it is easy to become
both solemn and heavy about Fitzgerald, man
and work. Perhaps there should be some
licensing procedure that would prevent bad
writers, pretentious and heavy scholars, from
dealing with Fitzgerald. Lacking that, a reader
can be grateful that, despite some notable
exceptions, students as well as professional
critics seem attracted to Fitzgerald out of a
common respect for his prose style and the
storyteller’s art. Like Fitzgerald’s work, much of
Fitzgerald criticism is distinguished by
extraordinary felicity of expression.
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Æ
B
11
349
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CHAPTER 14 / PRACTICE PSAT 1
1
350
Æ
65
z1
70
MC GRAW-HILL’S PSAT/NMSQT
Finally, Fitzgerald will probably continue to
claim the interest of both the general reader
and the scholar-critic. The mysteries of his
genius, like the mysteries of his style, remain to
be pondered. As our own perspectives change,
his various works will be seen in different lights.
The final test of Fitzgerald, as of all writers,
is that others want to read his works and to
share the pleasures they receive.
B
13
The first paragraph of Passage 1 reveals that
the author of Passage 1
(A) has recently been introduced to Fitzgerald’s novels
(B) has met F. Scott Fitzgerald personally
(C) has been critical of many of Fitzgerald’s
earlier works
(D) is writing an introduction to a book of
literary criticism
(E) is a novelist
Passage 2
After a brief revival, the novels of Scott
Fitzgerald seem destined again for obscurity,
labeled this time, by their most recent critics, as
75 darkly pessimistic studies of America’s spiritual
and ideological failures. The Great Gatsby, we
are now told, is not simply a chronicle of the
Jazz age but rather a dramatization of the
betrayal of the naı̈ve American dream in a
80 corrupt society.
From the start, Fitzgerald’s personal dreams
of romance contained the seeds of their own
destruction. In his earliest works, his optimistic
sense of the value of experience is
85 overshadowed by a personal intuition of
tragedy; his capacity for naı̈ve wonder is
chastened by satiric and ironic insights which
make surrender to the romantic impulse
incomplete. Though able to idealize the
90 sensuous excitement of an exclusive party or a
lovely face, Fitzgerald could not ignore the
speciosity inherent in the romantic stimuli of
his social world—in the unhurried gracious
poise that money can buy.
95
At the same time that Fitzgerald perceived
the melancholy nature of romantic illusion, his
attitude towards the rich crystallized. The thirst
for money is a crucial motive in Gatsby as in
Fitzgerald’s other novels, and yet none of his
100 major characters are materialists, for money is
never their final goal. The rich are too
accustomed to money to covet it. It is simply the
badge of their “superiority” and the justification
of their consuming snobberies.
105
Inevitably then, Fitzgerald saw his romantic
dream threaded by a double irony. Those who
possess the necessary means lack the will,
motive, or capacity to pursue a dream. Those
with the heightened sensitivity to the promises
110 of life have it because they are the disinherited,
forever barred from the white palace where “the
king’s daughter, the golden girl” awaits “safe
and proud above the struggles of the poor.”
B
14
As it is used in line 13, “refined” most nearly
means
(A)
(B)
(C)
(D)
(E)
B
15
processed
formal
concerned with minor details
challenging
pure
The author of Passage 1 mentions Edmund
Wilson in line 23 as an example of one who
(A) has deeply explored the tragic implications of Fitzgerald’s novels
(B) has written novels that were inspired by
Fitzgerald’s work
(C) has criticized certain themes in
Fitzgerald’s novels
(D) recognizes a quality in Fitzgerald’s works
that others may overlook
(E) focuses excessively on irrelevant aspects
of Fitzgerald’s style
B
16
In line 30, the phrase “charged with” most
nearly means
(A)
(B)
(C)
(D)
(E)
emboldened by
weakened by
given the responsibility of
electrified by
accused of
F. Scott Fitzgerald: A Collection of Criticism, Kenneth E. Eble,
#1973 McGraw-Hill, Passage 1: pp. 4– 6, Passage 2: pp. 60–
65. Copyright 1956 by the National Council of Teachers of
English. Reprinted with permission.
GO ON TO THE NEXT PAGE Å Å Å
17
The sentence “One learns” (line 48) is
intended primarily to convey the idea that
B
21
(A) Fitzgerald’s editors often destroyed his
best work
(B) college English classes should study
more of Fitzgerald’s lesser-known novels
(C) scholars should revisit Fitzgerald’s
novels many times
(D) most professors of literature enjoy
Fitzgerald’s prose
(E) literary craft includes a good deal of
reworking
B
18
B
19
In saying that “Fitzgerald’s personal dreams
of romance contained the seeds of their
own destruction” (lines 81 –83), the author
of Passage 2 means that
(A) Fitzgerald’s works have always lacked
popular appeal
(B) Fitzgerald’s life was cut tragically short
(C) Fitzgerald’s novels contain elements of
tragedy
(D) Fitzgerald was never satisfied with the
quality of his own work
(E) Fitzgerald’s romantic scenes were
unrealistic
B
20
(A) He would reluctantly agree because he
believes that readers are finding it
increasingly difficult to understand
Fitzgerald’s themes.
(B) He would strongly agree, because he
believes that Fitzgerald’s works are
fatally flawed.
(C) He would reluctantly disagree because
he believes that they will continue to be
a popular, but not a critical, success.
(D) He would strongly disagree because he
believes that Fitzgerald’s work will continue to have strong appeal.
(E) He would suggest that the statement is
irrelevant because the popularity of
Fitzgerald’s novels is not important.
The purpose of the fifth paragraph (lines
49 –62) of Passage 1 is primarily to express
the author’s concern about
(A) the unrestricted access to Fitzgerald’s
personal archives
(B) the tone and quality of some criticism
about Fitzgerald
(C) insufficient seriousness in criticism
about Fitzgerald
(D) the excessive quantity of criticism about
Fitzgerald
(E) the difference in quality between
the work of students and the work of
professional scholars
How would the author of Passage 1 likely
respond to the statement made in Passage 2
that “the novels of Scott Fitzgerald seem destined again for obscurity” (lines 72 –73)?
B
22
How does the “joy” (line 20) mentioned in
Passage 1 differ from the “wonder” (line 86)
mentioned in Passage 2?
(A) The “joy” is regarded as something that
makes Fitzgerald’s work distinctive,
while the “wonder” is regarded as being
compromised.
(B) The “joy” is regarded as insincere, while
the “wonder” is regarded as too blatant.
(C) The “joy” is regarded as a flaw in
Fitzgerald’s work, while the “wonder” is
regarded as a positive feature of his
work.
(D) The “joy” is regarded as something
unique in American literature, while the
“wonder” is regarded as being common
to most novels of the twentieth century.
(E) The “joy” is regarded as a feature of
Fitzgerald’s life, while the “wonder” is
regarded as a feature of Fitzgerald’s
work, but not his life.
The “white palace” (line 111) represents
(A)
(B)
(C)
(D)
(E)
the distinctive status of writers
moral superiority
literary perfection
a life of privilege
power acquired by force
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Æ
B
351
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CHAPTER 14 / PRACTICE PSAT 1
1
352
B
23
Æ
z1
MC GRAW-HILL’S PSAT/NMSQT
Which statement would most likely be supported by the authors of both passages?
(A) Some critics of Fitzgerald’s work have
focused on the tragic implications of his
novels.
(B) Fitzgerald’s works are even more popular
today than they were in his time.
(C) The characters in The Great Gatsby are
materialists.
(D) Fitzgerald’s works are far more optimistic than many believe.
(E) Scholarship on Fitzgerald’s works should
focus more on their style than on their
themes.
STOP
B
24
How would the author of Passage 1 likely
respond to the analysis of Fitzgerald’s work
presented in lines 81 –94?
(A) He would disagree with its claim that
Fitzgerald had a “capacity for naı̈ve
wonder.”
(B) He would agree with its focus on irony.
(C) He would regard it as an unnecessary
focus on the tragic aspects of Fitzgerald’s
works.
(D) He would regard it as insufficiently critical of Fitzgerald’s choice of theme.
(E) He would suggest that it ignores important details about Fitzgerald’s personal
life that would explain the themes in his
works.
You may check your work, on this
section only, until time is called.
CHAPTER 14 / PRACTICE PSAT 1
353
Section 2
Time—25 minutes
Æ
20 Questions
z
2
Directions for Multiple-Choice Questions
In this section, solve each problem, using any available space on the page for scratchwork. Then decide
which is the best of the choices given and fill in the corresponding oval on the answer sheet.
.
.
.
You may use a calculator on any problem. All numbers used are real numbers.
Figures are drawn as accurately as possible EXCEPT when it is stated that the figure is not drawn
to scale.
All figures lie in a plane unless otherwise indicated.
Reference Information
The arc of a circle measures 3608.
Every straight angle measures 1808.
The sum of the measures of the angles in a triangle is 1808.
B
1
The area of a rectangle with a height of 4 cm
and a base of 6 cm is how many times greater
than the area of a triangle with a height of
4 cm and a base of 4 cm?
(A)
(B)
(C)
(D)
(E)
B
4
(A)
(B)
(C)
(D)
(E)
1
1.5
2
2.5
3
B
5
B
2
If x ¼ 2y þ 2, how much greater is 6x than
12y?
(A)
(B)
(C)
(D)
(E)
B
3
2
6
8
12
24
How many integers between 10 and 40 are
divisible by both 2 and 6?
(A)
(B)
(C)
(D)
(E)
Two
Three
Four
Five
Six
If it is now 4:30 p.m., what time will it be
exactly 100 hours from now?
4:30 p.m.
8:30 p.m.
12:30 a.m.
2:30 a.m.
4:30 a.m.
Carrie, Denise, and Emily sold a total of 48
candy bars. If Emily sold four times as
many candy bars as Denise did, and Denise
sold three times as many candy bars as
Carrie did, how many candy bars did
Denise sell?
(A)
(B)
(C)
(D)
(E)
3
6
9
12
15
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354
MC GRAW-HILL’S PSAT/NMSQT
B
B
6
9
2x°
Æ
z2
3x°
In a certain homeroom, the number of girls is
6 less than twice the number of boys. If the
class contains b boys, which of the following
would express the total number of students
present in the class if 2 girls were absent?
(A)
(B)
(C)
(D)
(E)
y°
Note: Figure not drawn to scale.
2b 2 8
2b 2 4
3b 2 8
3b 2 6
3b 2 4
In the figure above, what is the value of y?
(A)
(B)
(C)
(D)
(E)
B
7
72
60
48
36
40
B
10
(A)
(B)
(C)
(D)
(E)
Let the function f (x) be defined by the
equation f(x) ¼ 2x 2 x 2. Which of the following has a positive value?
(A)
(B)
(C)
(D)
(E)
If (x þ 5)2 ¼ 0,
(x 2 1)(x þ 1)?
B
what
is
the
value
of
226
224
0
24
26
11
f (0.5)
f (0)
f (20.5)
f (21.5)
f (22.5)
l
A
B
C
B
8
y
Note: Figure not drawn to scale.
In the figure above, the circle with center at C
has a circumference of 6p. If line ‘ is tangent
to the circle and AB ¼ 4, what is the distance
from B to C?
l
1
(A)
(B)
(C)
(D)
(E)
x
O
1
What is the equation of line ‘ in the figure
above?
4.8
5.0
6.2
7.0
7.2
(A) y ¼ 2x þ 3
1
(B) y ¼ x þ 3
2
1
(C) y ¼ x þ 6
2
1
(D) y ¼ x þ 3
2
(E) y ¼ 2x þ 6
B
12
A set consists of five consecutive integers.
The sum of these integers is 210. What is
the greatest possible product that can be
obtained by multiplying three different integers from this set?
(A)
(B)
(C)
(D)
(E)
224
26
0
6
24
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13
The first day of a 30-day month is a Monday.
Which of the following is closest to the probability that a day picked at random from this
month will be a Wednesday?
(A)
(B)
(C)
(D)
(E)
B
14
0.03
0.07
0.10
0.13
0.17
B
17
B
18
If jxj . 2, which of the following statements
must be true?
I. x . 0
II. x 2 . 2
III. x 3 . 2
(A)
(B)
(C)
(D)
(E)
B
15
B
19
A jar contains only red, white, and blue
marbles. If the number of red marbles is 56
the number of white marbles, and the
6
number of red marbles is the number of
7
blue marbles, what is the least possible
number of marbles in the jar?
(A)
(B)
(C)
(D)
(E)
16
B
II only
I and II only
I and III only
II and III only
I, II, and III
The graph of which of the following points is
2
below the graph of the line y ¼ x þ 1?
3
(A) (21, 1)
(B) (1, 1)
(C) (1, 2)
(D) (3, 3)
(E) (4, 4)
If 3n21 ¼ 2721, then n ¼
(A)
(B)
(C)
(D)
(E)
23
22
21
1
2
1
¼ y, where x = 0, which of the
x
1
following expresses x2 þ 2 in terms of y?
x
(A) y 2 þ 2
(B) y 2 þ 1
(C) y 2
(D) y 2 2 1
(E) y 2 2 2
If x þ
B
20
y
l
A
18
72
101
113
123
O
(16,0)
8, a, b, 27
(6,0)
In the sequence above, each term, except the
first, is equal to the previous term times a
b
constant. What is the value of ?
a
(A) 1.125
(B) 1.50
(C) 3.375
(D) 4.75
(E) 6.33
Note: Figure not drawn to scale.
STOP
x
If line ‘ in the figure above has a slope of 2,
what are the coordinates of point A?
(A)
(B)
(C)
(D)
(E)
(0, 7.2)
(0, 13.2)
(0, 14.4)
(0, 18.4)
(0, 19.2)
You may check your work, on this
section only, until time is called.
Æ
B
355
z
CHAPTER 14 / PRACTICE PSAT 1
2
356
MC GRAW-HILL’S PSAT/NMSQT
Section 3
Time—25 minutes
24 Questions (25– 48)
Æ
z3
Each of the sentences below is missing one or two portions. Read each sentence. Then select the choice
that most logically completes the sentence, taking into account the meaning of the sentence as a whole.
Example:
Rather than accepting the theory unquestioningly, Deborah regarded it with -- ----.
(A)
(B)
(C)
(D)
(E)
mirth
sadness
responsibility
ignorance
skepticism
Correct response: (E)
B
25
Unlike most farmers, who regarded rain as a
great benefit, Harold often regarded it as
--- ---.
(A)
(B)
(C)
(D)
(E)
B
26
B
27
28
an abundance
a hardship
a scheme
a response
a distortion
Pablo Picasso is considered - --- -- of artistic
perfectionism because he would destroy any
of his works that he considered -- ----.
(A)
(B)
(C)
(D)
(E)
B
an enemy . . poor
an example . . beautiful
a paragon . . mediocre
a proponent . . aesthetic
an advocate . . monetary
The store employees tried to -- --- - the angry
shoppers with offers of discounted merchandise and free gift wrapping.
(A)
(B)
(C)
(D)
(E)
B
29
exculpate
impede
mollify
pilfer
abridge
Some European governments are concerned
that severe immigration restrictions, while
rendering nations less --- --- to foreign terrorists, would also - --- -- the influx of creative
ideas from abroad.
(A)
(B)
(C)
(D)
(E)
pervious . . stem
impregnable . . halt
durable . . promote
penetrable . . hasten
potent . . restrict
Joseph often picked fights with anyone who
challenged his ideas, until his friends made
it clear that such --- --- was unacceptable.
(A)
(B)
(C)
(D)
(E)
belligerence
diligence
fortitude
restraint
eloquence
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
Questions 32–33 are based on the
following passage.
5
Questions 30– 31 are based on the
following passage.
Line
5
10
15
20
B
30
B
31
Historical evidence takes many forms,
including oral traditions and archaeology as
well as written texts. Study of the very distant
past necessarily relies primarily on oral
traditions and archaeology; these two kinds of
evidence offer different perspectives on the past
and answer different historical questions. Oral
tradition is the means by which knowledge—
both fact and myth—was passed on until it was
written down. Archaeology, in contrast, is the
scientific study of the material remains of past
human life and activities: fossil relics, artifacts,
and monuments. Archaeology supplies physical
evidence of material culture, while oral sources
provide insight into the nonmaterial world of
ideas, values and beliefs. Archaeological
investigation may present evidence from
millions of years before the present or from the
most recent historical past. Oral traditions,
some of which are ultimately written down, are
more ephemeral, extending across a single
lifetime or as far back as the past 10,000 years
or so of remembered human experience.
10
15
20
25
B
32
The primary purpose of this passage is to
(A) promote the study of archaeology
(B) describe different oral traditions
(C) discuss a few important historical discoveries
(D) compare two means of gathering information
(E) suggest an improvement to the study of
archaeology
The passage indicates that the “nonmaterial
world of ideas, values and beliefs” (lines
15 –16) is
(A) a subject that only archaeologists can
study
(B) not sufficiently emphasized in historical
texts
(C) an unreliable source of historical
evidence
(D) evidence of material culture
(E) the substance of oral tradition
B
33
After having—with agony and despair—
lived through the irrational tidal waves of the
last big war, the world of planners settled down
to a rose-colored rational optimism: “To give
education, food and health care would suffice
to bring peace and stability to this world;
satisfying the ‘basic needs’ for information and
acceptable material living conditions would
guarantee mutual understanding and
democratic tolerance within and between
nations.” This belief has been badly shaken by
now; we are beginning to see that man is not
rational enough to make the expected use of the
improvements achieved in the last 30 years,
that unrest, prejudice, ideological distortion,
and violence do not come from the poor (who
might have most reason for such reactions), but
to a considerable extent from the well-cared-for
and well-educated classes in many nations—by
no means always the most underdeveloped
ones—of the world. We discover that reality
does not conform to our rational prescriptions,
and we are forced to ponder whether our
present level of rationality is at all adequate for
dealing with the problems of our world.
This passage most directly criticizes
(A)
(B)
(C)
(D)
(E)
poverty
war
dishonesty
irrationality
technology
The parenthetical comment in lines 16 –17
indicates that the poor
(A) are ignored by the more affluent classes
(B) should be granted more political power
(C) are more justified than the wealthy in
acting rebelliously
(D) should be the focus of postwar planning
(E) have talents that are underappreciated in
modern societies
First paragraph: In the Balance: Themes in Global History, Candice
L. Goucher, Charles A. Le Guin, Linda A. Walton, #1998
McGraw-Hill, p xxxi
Second paragraph: Culture and Industrialization: An Asian
Dilemma, Rolf E. Vente, Peter S.J. Chen, #1980 McGraw-Hill,
p 52
GO ON TO THE NEXT PAGE Å Å Å
Æ
Line
z
Each passage below is followed by one or two
questions based on its content. Answer each
question based on what is stated or implied
in the passage that precedes it.
357
3
358
MC GRAW-HILL’S PSAT/NMSQT
Questions 34 – 40 are based on the
following passage.
The following is an excerpt from a story written
by a twentieth-century Yugoslav writer.
Æ
Line
z3
5
10
15
20
25
30
35
40
45
50
I like to get up early and go down to sit on
my bench by the bank of the river just at the
crack of dawn, before even the sparrows are
awake and before the traffic has begun to make
its daily assault on my nerves. The men with
hoses have just set out to clean the pavements,
everything is quiet and happy, just as it must
have looked a million years ago. The river
gurgles along, clean and gay, rejoicing at its
brief moment of rest before the beginning of
another exhausting day. I’m no hermit or
misanthrope. Just every now and again I get fed
up with everything, and I mean everything, and I
feel the need to be alone, completely alone. But
not for long, for in fact without that
“everything,” I can’t get along either. People
and things simply get me down; maybe because
both are human products, and there’s
something of that exhausted human core that
remains in them too. And so I start to want to
change. The fashionable word for it is
recreation. We used to have our own word for
it. Maybe it doesn’t convey everything that the
foreign one does, but in any case none of that is
so very important as long as a man does have a
rest and get his strength back regularly. That’s
the thing that we haven’t managed to pull out of
our dusty old dictionaries. Anyway, I go off
down to the river to get my strength back. And
that’s really what happens; I come to life again.
I may have come to our appointment with a
heavy, care-worn head, or I may have been
thinking all the way about what I might do to
avoid this or that; still when I arrive, my body
seems to become light and my mind keen; and
the river’s quiet friendly voice restores the joy
and hope that had fled before trivial everyday
anxieties and become hidden away in the
darkest gloom. I’ve seldom met anyone who has
answered my question with anything other
than that threadbare “very well,” and a “very
well” so bloodless and feeble that you feel
wretched yourself and don’t want to ask again.
That plague of very well has spread so far, that
whenever I feel there’s so much of it mounting
up inside me that it’s starting to choke me, I go
off to have a chat with the river. Only then am I
capable of looking inside myself, bathed,
refreshed, cleansed (not of sin, I didn’t want to
imply that). And I feel then just how much I’ve
forgotten myself, lost myself somewhere along
the way, mislaid an illusion or two, and
altogether subordinated myself to external
obsessions and barren desires.
55
I try to prove to myself, starting always right
at the beginning, that that’s life as well, that
everyday toil and moil, that perpetual bustle
and panicky attention to the implacable
dictates of the hands of a clock, that “hello,
60 how’s it going, be seeing you, in a hurry” tossed
off in passing . . . somehow I manage to put
together the pro et contra, get back my balance,
and make use of that skill a man has for always
finding a way of compromising with himself.
65 But it’s really only putting off the main issue.
Putting off and putting off, a constant flight
from open conflict, cowardice.
That much-praised business of working has
become an end in itself, work for work’s sake, a
70 sort of undefined elemental need to shake out
some “surplus life,” to exploit one’s own self. It’s
lost its original meaning long since its primeval,
ennobling, creative function; it shouldn’t really
be called work any longer, we ought to find
75 another word for it.
Fortunately, this mood passes. The wood
right over on the other side that comes down
to the water’s edge doesn’t let me sink too
far down this particular slough. Like green
80 lightning, it flashes before me and disperses
these black thoughts like so much dust.
When the city starts waking up behind me, I
know that the alloted time of my appointment
with the river has expired. It ceases to be mine
85 and only mine, and becomes an ordinary,
broad, flat river; tugs harnessed in steel cables
crawl and struggle upstream towards some
destination and fishing boats float aimlessly
about; if there is a wind, a yacht or two can be
90 seen. Pensioners come crawling out to their
favorite bench, children set up a hubbub in a
nearby school-yard, waiters in the restaurant
built right over the water begin to discreetly
clink crockery and cutlery. The day begins.
95
I go off without looking back. The market I
pass through is brimming with life, peasants
and housewives on all sides. Slowly I make my
way home. Invariably I meet some
acquaintance on the way. From the distance, I
100 can see him smiling. If he has the time, he’ll
stop to shake hands, but usually we don’t shake
hands, he just flicks “Hello, how are you?” at me
as he passes, and smiles, and I smile and say
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
37
In line 66, the word “flight” most nearly
means
(A)
(B)
(C)
(D)
(E)
B
38
In the third paragraph (lines 68 –75) the narrator suggests that long ago, unlike now,
work was
(A)
(B)
(C)
(D)
(E)
B
34
35
food
reminiscence
information
anxiety
rejuvenation
The sentence in lines 14 –16 (“But not for . . . I
can’t get along either) indicates that the
narrator
(A) has been receiving professional therapy
(B) is not well understood by his peers
(C) is often frustrated by his inability to get
away from people
(D) needs those aspects of his life that
occasionally oppress him
(E) has been coming to the river for many
years
B
36
more challenging
not necessary for survival
a social experience
a creative endeavor
performed in nature
The first paragraph indicates that, to the narrator, the river is primarily a source of
(A)
(B)
(C)
(D)
(E)
B
obligation
fleeing
jumping
floor
swarm
B
39
The “pensioners” (line 90) are mentioned as
examples of people who
(A)
(B)
(C)
(D)
(E)
B
40
do not appreciate the beauty of the river
speak in a perfunctory manner
are obsessed with work
have a balanced perspective on life
have disrupted the narrator’s solitude
The conflict in this passage is primarily
between
(A)
(B)
(C)
(D)
(E)
solitude and sociability
the past and the future
life and death
desire and virtue
wealth and poverty
Which of the following is the closest to “the
thing that we haven’t managed to pull out
of our dusty old dictionaries” (lines 27 –28)?
(A)
(B)
(C)
(D)
(E)
emotion
weakness
restoration
verbalization
assault
To Icarus and Not to the Sun, Reka, 65 Short Stories, Yugoslav
Illustrated Monthly, 1970, pp. 235– 236
GO ON TO THE NEXT PAGE Å Å Å
Æ
B
z
“Very well, thanks and what about you?” and he
105 says something in reply, and I suddenly get the
desire to run after him and catch him up and
look at him closely, really eyeball to eyeball, to
see if he’s still smiling as cheerfully as he was
when he was that far away, and I stand still for a
110 moment in indecision and look around. He’s
long way off, too far for it to be worthwhile
chasing after him, you can never catch up with
anyone anyway.
So I just keep going in the same direction,
115 smiling to myself. Today I’ve been down to the
river.
359
3
360
MC GRAW-HILL’S PSAT/NMSQT
Questions 41 – 48 are based on the
following passage.
The following is an excerpt from an article about
Immanuel Kant, an eighteenth-century British
philosopher.
Æ
z3
According to Kant, his reading of David
Hume awakened him from his dogmatic
Line slumber and set him on the road to becoming
the “critical philosopher,” whose position can
5 be seen as a synthesis of the Leibniz-Wolffian
rationalism and the Humean skepticism. Kant
termed his basic insight into the nature of
knowledge “the Copernican revolution in
philosophy.”
10
Instead of assuming that our ideas, to be
true, must conform to an external reality
independent of our knowing, Kant proposed
that objective reality is known only insofar as it
conforms to the essential structure of the
15 knowing mind. He maintained that objects of
experience—phenomena—may be known, but
that things lying beyond the realm of possible
experience—noumena, or things-inthemselves—are unknowable, although their
20 existence is a necessary presupposition.
Phenomena that can be perceived in the pure
forms of sensibility, space, and time must, if
they are to be understood, possess the
characteristics that constitute our categories of
25 understanding. Those categories, which
include causality and substance, are the source
of the structure of phenomenal experience.
The scientist, therefore, may be sure only
that the natural events observed are knowable
30 in terms of the categories. Our field of
knowledge, thus emancipated from Humean
skepticism, is nevertheless limited to the world
of phenomena. All theoretical attempts to know
things-in-themselves are bound to fail. This
35 inevitable failure is the theme of the portion of
the Critique of Pure Reason entitled the
“Transcendental Dialectic.” Here Kant shows
that the three great problems of metaphysics—
God, freedom, and immortality—are insoluble
40 by speculative thought. Their existence can be
neither affirmed nor denied on theoretical
grounds, nor can they be scientifically
demonstrated, but Kant shows the necessity of
a belief in their existence in his moral
45 philosophy.
Kant’s ethics centers in his categorical
imperative (or moral law)—“Act as if the
maxim from which you act were to become
through your will a universal law.” This law has
50
55
60
65
70
75
B
41
its source in the autonomy of a rational being,
and it is the formula for an absolutely good will.
However, since we are all members of two
worlds, the sensible and the intelligible, we do
not act infallibly in accordance with this law
but, on the contrary, almost always act
according to inclination. Thus what is
objectively necessary, i.e., to will in conformity
to the law, is subjectively contingent; and for
this reason the moral law confronts us as an
“ought.”
In the Critique of Practical Reason Kant
went on to state that morality requires the
belief in the existence of God, freedom, and
immortality, because without their existence
there can be no morality. In the Critique of
Judgment Kant applied his critical method to
aesthetic and teleological judgments. The chief
purpose of this work was to find a bridge
between the sensible and the intelligible worlds,
which are sharply distinguished in his
theoretical and practical philosophy. This
bridge is found in the concepts of beauty and
purposiveness that suggest at least the
possibility of an ultimate union of the two
realms.
The passage suggests that Kant found David
Hume’s philosophy to be
(A)
(B)
(C)
(D)
(E)
B
42
logically unfounded
inspirational
open-minded
morally repugnant
charmingly naı̈ve
The author uses the term “dogmatic
slumber” (line 2) to suggest that
(A) Hume wrote very dull prose.
(B) Kant was a controversial political figure.
(C) Kant was more intellectually rigid before
reading Hume.
(D) Kant found Hume’s writing to be
humorous.
(E) Hume wrote many more books than
Kant did.
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
According to the passage, the major theme of
the “Transcendental Dialectic” is that
(A)
(B)
(C)
(D)
(E)
B
44
45
46
one cannot know things-in-themselves
ethical behavior is unique to humans
the existence of God can be proved
people should be optimistic
philosophers must take a more scientific
approach
The author implies that we “do not infallibly
act in accordance with this law” (lines 53 –54)
because we
(A) are innately selfish
(B) cannot escape the subjectivity of human
experience
(C) are concerned more with beauty than
morality
(D) do not understand the history of the law
(E) do not have completely free will
According to the passage, Kant’s Critique of
Pure Reason suggests that free will is
(A)
(B)
(C)
(D)
(E)
B
B
B
47
an illusion
gained only through struggle
a requirement of ethical behavior
knowable as a thing-in-itself
an attribute of all living things
One who behaves strictly according to
Kant’s “categorical imperative” (lines 46 –
47) necessarily believes that any valid moral
law should
(A)
(B)
(C)
(D)
(E)
STOP
48
(A)
(B)
(C)
(D)
(E)
skeptical philosophy and optimism
ethics and aesthetics
the past and the future
the philosopher and the common person
things that can be perceived and things
that can be understood
The primary purpose of the final paragraph
is to
(A) address an objection to Kant’s
philosophy
(B) illustrate Kant’s impact on later
philosophers
(C) explain the origin of Kant’s beliefs
(D) describe further works of Kant
(E) qualify a claim made in the previous
paragraph
apply to all human beings
be determined by religious dictate
be submitted to scientific testing
derive from a democratic process
change according to the situation
“Kant, Immanuel,” Columbia Encyclopedia, Sixth
New York: Columbia University Press, #2001-2004
B
The “bridge” in line 68 is a bridge between
Edition,
You may check your work, on this
section only, until time is called.
Æ
43
z
B
361
3
362
MC GRAW-HILL’S PSAT/NMSQT
Section 4
Time—25 minutes
18 Questions (21– 38)
Directions for Multiple-Choice Questions
Æ
z4
In this section, solve each problem, using any available space on the page for scratchwork. Then decide
which is the best of the choices given and fill in the corresponding oval on the answer sheet.
.
.
.
You may use a calculator on any problem. All numbers used are real numbers.
Figures are drawn as accurately as possible EXCEPT when it is stated that the figure is not drawn
to scale.
All figures lie in a plane unless otherwise indicated.
Reference Information
The arc of a circle measures 3608.
Every straight angle measures 1808.
The sum of the measures of the angles in a triangle is 1808.
B
21
If a square has a perimeter of 20 centimeters,
what is one-half its area, in square
centimeters?
(A)
(B)
(C)
(D)
(E)
B
22
B
23
10
12.5
20
25
50
Which of the following numbers is equal to
one-third of its square?
1
(A)
9
1
(B)
3
(C) 3
(D) 6
(E) 9
Checkers are stacked into four piles such that
each pile has k more checkers than the previous pile. If the first pile contains 3 checkers,
and there are 30 checkers in total in the four
piles, what is the value of k?
(A)
(B)
(C)
(D)
(E)
B
24
2
3
4
5
6
What number is equal to
(A)
(B)
(C)
(D)
(E)
3
of itself plus 240?
5
144
280
360
400
600
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
Total Sales of Different Book Genres
(in thousands)
Nonfiction
500
x°
Self-help
325
Fiction
375
B
27
If 2n ¼
(A)
(B)
(C)
(D)
(E)
2
, what is the value of n þ k?
2k
22
21
0
1
2
Æ
25
B
28
z
B
363
4
The pie graph above shows the book sales for
a publishing company in a single year. If x
represents the measure, in degrees, of the
central angle of the sector representing the
sales of nonfiction books, what is the value
of x?
(A)
(B)
(C)
(D)
(E)
B
26
120
125
135
145
150
Set S consists of 10 consecutive even integers
that have an average (arithmetic mean) of 23.
Which of the following must be true?
I. The median of set S is 23.
II. No two integers in set S have a difference
greater than 10.
III. There are no multiples of 5 in set S.
(A)
(B)
(C)
(D)
(E)
The pyramid in the figure above has a square
base and four congruent triangular faces. If
the area of the base is 144 square inches
and the height of the pyramid is 8 inches,
what is the area of one of the triangular
faces, in square inches?
(A)
(B)
(C)
(D)
(E)
42
48
60
96
120
I only
II only
I and II only
I and III only
I, II, and III
GO ON TO THE NEXT PAGE Å Å Å
364
MC GRAW-HILL’S PSAT/NMSQT
Directions for Student-Produced Response Questions
Each of the questions in this section requires you to solve the problem and enter your answer in a grid, as
shown below.
.
If your answer is 2/3 or .666 . . . , you must enter the most accurate value the grid can accommodate, but you may do this in one of four ways:
.
In the example above, gridding a response of 0.67 or 0.66 is incorrect because it is less accurate than
those above.
The scoring machine cannot read what is written in the top row of boxes. You MUST fill in the
numerical grid accurately to get credit for answering any question correctly. You should write
your answer in the top row of boxes only to aid your gridding.
1
31
Do not grid in a mixed fraction like 3 as 3 1 / 2 because it will be interpreted as . Instead,
2
2
convert it to an improper fraction like 7/2 or a decimal like 3.5 before gridding.
Æ
z4
.
.
.
.
.
.
.
.
B
29
None of the answers will be negative, because there is no negative sign in the grid.
Some of the questions may have more than one correct answer. You must grid only one of the correct
answers.
You may use a calculator on any of these problems.
All numbers in these problems are real numbers.
Figures are drawn as accurately as possible EXCEPT when it is stated that the figure is not drawn
to scale.
All figures lie in a plane unless otherwise indicated.
1
1
What is the result when of 80 is divided by
4
3
of 90?
B
31
x°
x°
y°
x°
Note: Figure not drawn to scale.
B
30
For all real numbers x and y, let x ø y be
defined by the equation
x ø y ¼ (x þ y)(x 2 y). What is the value
of 5 ø 3?
In the figure above, if x ¼ 89, what is the
value of y?
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
If the maximum value in the range of the
function y ¼ f (x) is 6, what is the maximum
value in the range of the function
y ¼ 3f (x 2 1)?
B
36
y
Q
(0, 6)
B
33
m ¼ 4A3
O
n ¼ 7B9
Suppose m and n are 3-digit integers, as
shown, where A and B represent digits. If m
is divisible by 3 and n is divisible by 9, what
is the greatest possible value of m þ n?
B
34
If 2mþ1 ¼ 84, what is the value of m?
B
m, n, 9, 5
If the product of the four numbers above is 0
and the median of these four numbers is 3.5,
what is the average (arithmetic mean) of
these four numbers?
STOP
x
Note: Figure not drawn to scale.
In the figure above, if the shaded rectangle
has an area of 90 square units, what is the
slope of line PQ (not shown)?
B
37
A water pump, working at a constant rate,
fills 27 of a tank in 1 13 hours. What fraction of
the tank will be filled, at this rate, after
3 hours?
B
A box contains only red, blue, and yellow
crayons. The ratio of red crayons to blue
crayons is 2:3, and the ratio of blue crayons
to yellow crayons is 2:1. If there is a whole
number of each color of crayon in the box,
what is the probability that a crayon chosen
randomly from the box is blue?
38
35
P (3, 0)
You may check your work, on this
section only, until time is called.
Æ
32
z
B
365
4
366
MC GRAW-HILL’S PSAT/NMSQT
Section 5
Time—30 minutes
39 Questions (1– 39)
Directions for “Improving Sentences” Questions
Each of the sentences below contains one underlined portion. The portion may contain one or more
errors in grammar, usage, construction, precision, diction (choice of words), or idiom. Some of the
sentences are correct.
Æ
Consider the meaning of the original sentence, and choose the answer that best expresses that meaning.
If the original sentence is best, choose (A), because it repeats the original phrasing. Choose the phrasing
that creates the clearest, most precise, and most effective sentence.
z5
EXAMPLE:
The children couldn’t hardly believe their eyes.
(A)
(B)
(C)
(D)
(E)
B
1
couldn’t hardly believe their eyes
would not hardly believe their eyes
could hardly believe their eyes
couldn’t nearly believe their eyes
could hardly believe his or her eyes
When used intelligently, you can use
mnemonics to help you to memorize cumbersome facts.
(A) you can use mnemonics to help you to
memorize cumbersome facts
(B) cumbersome facts can be memorized
with the use of mnemonics
(C) mnemonics can help you to memorize
cumbersome facts
(D) you can memorize cumbersome facts
more easily with mnemonics
(E) cumbersome facts are more easily memorized by using mnemonics
B
2
The annual conference, traditionally used as
a forum for presenting new research,
instead this year dedicated to resolving theoretical disputes.
(A)
(B)
(C)
(D)
(E)
instead this year dedicated to
was instead this year dedicated to
being dedicated this year instead to
was instead dedicated for this year
instead was dedicated toward this year
B
3
Jenna went to have her arm examined by the
doctor, which was the time when she was
told by him that she would not be able to
play soccer for at least six weeks.
(A) which was the time when she was told by
him
(B) which was when she was told by him
(C) that then told her
(D) at which time she was told
(E) who told her
B
4
The effects of a flu epidemic, possibly being
exacerbated by social conditions because of
the fact that the virus spreads quickly when
people live in close quarters.
(A) epidemic, possibly being exacerbated by
social conditions because of the fact that
(B) epidemic are possibly exacerbated by
social conditions due to the fact of
(C) epidemic can be exacerbated by social
conditions, because
(D) epidemic, possibly being exacerbated by
social conditions because
(E) epidemic can be exacerbated by social
conditions due the fact of
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
One aspect of the play that receives universal
acclaim is it analyzes a meaningful social
issue with insight while at the same time
humor.
(A) it analyzes a meaningful social issue with
insight while at the same time humor
(B) it uses humor and insight to analyze a
meaningful social issue
(C) it providing a humorous and insightful
analysis of a meaningful social issue
(D) its insightful yet humorous analysis of a
meaningful social issue
(E) its analysis of a meaningful social issue,
which is both insightful and humorous
B
6
7
8
B
9
being a realistic depiction of
it is like a realistic depiction of
a realistic depiction of
depicting realistically
realistic in its depiction of
The voyage was not as harrowing as the
captain later made it seem; in fact, the trade
winds were even stronger than they were predicted to be.
(A) seem; in fact, the trade winds were even
stronger than they were predicted to be
(B) seem; nevertheless the trade winds were
in fact stronger than predicted
(C) seem so the trade winds were even stronger than the prediction of them
(D) seem, the trade winds were even stronger
than they were predicted to be
(E) seem; the trade winds being even stronger than they were predicted to be
B
10
Although Jermaine had never played handball before, he moved around the court as if
playing all his life.
(A)
(B)
(C)
(D)
(E)
Campaigning for over ten consecutive
months, the Senator was glad to finally be
home with her family.
(A) Campaigning for over ten consecutive
months
(B) While campaigning for over ten consecutive months
(C) Over ten consecutive months in which
she was campaigning
(D) Being over ten consecutive months of her
campaigning
(E) Having campaigned for over ten consecutive months
The film is not so much a suspense thriller as
being a realistic depiction of modern
suburbia.
(A)
(B)
(C)
(D)
(E)
Carl Sagan’s engaging presentation of scientific concepts inspired many people who
had never before been interested in science.
(A) people who had never before been interested in science
(B) people and they had never been interested in science before
(C) people; previously they had not been
interested in science
(D) people, never having been interested in
science before
(E) people of whom they had not previously
been interested in science
B
B
B
11
if playing
having played
if from playing
if he would have been playing
if he had been playing
Many factors influence the price of crude oil,
including advancements in technology, patterns in the weather, and how the global
political climate changes.
(A) how the global political climate changes
(B) the changing nature of how the political
climate is
(C) changes in the global political climate
(D) how the political climate is changing
globally
(E) what the changes are in the global political climate
GO ON TO THE NEXT PAGE Å Å Å
Æ
5
z
B
367
5
368
B
12
MC GRAW-HILL’S PSAT/NMSQT
Four of the five symphonies performed in the
music festival showcased instruments from
the colonial era, particularly that of the
Mississippi Pastoral.
(A) festival showcased instruments from the
colonial era, particularly that of the
Mississippi Pastoral
(B) festival, particularly the Mississippi Pastoral, showcased instruments from the
colonial era
(C) festival showcased instruments from the
colonial era, which included especially
the Mississippi Pastoral
(D) festival, particularly the Mississippi Pastoral, showcasing instruments from the
colonial era
(E) festival, particularly the Mississippi Pastoral, as a showcase of instruments from
the colonial era
Æ
z5
B
13
B
15
(A) Brice’s stubbornness often caused her to
alienate her classmates
(B) Brice’s classmates were often alienated
by her being stubborn
(C) Brice being stubborn often alienated her
classmates
(D) Brice often alienated her classmates by
being stubborn
(E) and so Brice alienated her classmates
because of her stubbornness
B
16
and many though think it came from
and not, as many people think, in
but not, as many people think, from
not where people think it came from
but many people think it is
B
17
B
14
The course requires that students work a
great deal in the laboratory and which
includes weekly seminars in which they
discuss their findings.
(A) which includes weekly seminars in which
they discuss their findings
(B) discussions of their findings in weekly
seminars as well
(C) discuss their findings in weekly seminars
(D) discussing their findings in weekly seminars
(E) to discuss their findings in weekly seminars
The entire legal team had to spend nearly two
days revising the contracts to conform with
the new changes in the federal industrial
regulations.
(A) to conform with the new changes in
(B) for them conforming to the new changes
in
(C) in their conformance toward the new
changes of
(D) to get them to conform for the new
changes of
(E) in conforming to the new changes about
The pasta now known as spaghetti originated
in China and many though think it came
from Italy.
(A)
(B)
(C)
(D)
(E)
Having a stronger will than most preschoolers, Brice’s stubbornness often caused her
to alienate her classmates.
Those students who convince themselves
that they have the talent to become professional athletes, often neglecting their
studies because they feel they will never
need to use them.
(A)
(B)
(C)
(D)
(E)
athletes, often neglecting
athletes in often neglecting
athletes often neglect
athletes, and so often neglect
athletes would nevertheless often neglect
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
Seat belts were extremely unpopular when
they were first introduced by Ford Motors,
but for those who used them they saved hundreds of lives.
(A) for those who used them they saved hundreds of lives
(B) they saved the lives of hundreds of those
who used them
(C) the ones that used them had hundreds of
their lives saved by them
(D) hundreds of the ones who used them had
their lives saved by them
(E) hundreds of lives were saved of those
who were the ones using them
B
19
The demand for American goods and services
increases as the value of the dollar decreases
and because of the lowering of trade barriers.
(A)
(B)
(C)
(D)
(E)
B
20
because of the lowering of trade barriers
in the lowering of trade barriers
lower trade barriers
for lower trade barriers
as trade barriers are lowered
The professional hockey strike has most
acutely affected the officials, most of them
depend on the seasonal work for their
livelihood.
(A)
(B)
(C)
(D)
(E)
of them depend
of them have been depending
which depend
of whom depend
depend
Directions for “Identifying Sentence Error” Questions
The following sentences may contain errors in grammar, usage, diction (choice of words), or idiom.
Some of the sentences are correct. No sentence contains more than one error.
If the sentence contains an error, it is underlined and lettered. The parts that are not underlined are correct.
If there is an error, select the part that must be changed to correct the sentence.
If there is no error, choose (E).
EXAMPLE:
By the time they reached the halfway point
A
in the race, most of the runners hadn’t hardly
B
C
D
begun to hit their stride. No error
E
B
21
Thomas Jefferson invented the dumbwaiter
A
in 1795, and they have been used ever since
C
B
as a valuable labor-saving device. No error
E
D
B
The sudden rush of investors to withdraw
A
their money from their accounts caused
B
C
many banks to have closed their doors for
D
several weeks. No error
E
22
B
23
Charles Evans Hughes was not only
A
an exemplary Chief Justice of the Supreme
B
Court and also was a governor of New York
C
and the Republican candidate for president
D
in 1916. No error
E
GO ON TO THE NEXT PAGE Å Å Å
Æ
18
z
B
369
5
370
B
24
B
25
Æ
z5
B
26
MC GRAW-HILL’S PSAT/NMSQT
The dramatic geometric design
of the arboretum, which was a stark
A
B
departure from the naturalism of
C
traditional English gardens, attest to
D
Colcott’s love of order and beauty. No error
E
Although the delay in the deployment of
A
troops was a tactful blunder, it did not
B
C
diminish the effectiveness of the general’s
D
overall strategy. No error
E
The conference delegates were astonished
A
not only by the sheer number of protestors,
B
but also by the smooth coordination of the
D
C
many simultaneous demonstrations.
B
30
B
The professors usually never cancel classes,
A
even when there is a snowstorm, because
B
they believe that knowledge is too important
to compromise for anything but the most
D
C
dire circumstances. No error
E
B
28
B
29
Helene found it hard to believe that a
A
student as diligent as her could ever be
B
singled out as an example of laziness.
D
C
No error
E
more likely that a child will be born male
B
A
than female, the higher mortality rate of
C
males ensures that the number of adult men
and women will be about the same at reproD
ductive age. No error
E
B
31
Only in the last several years has the econB
A
omic ministers of the neighboring countries
come to realize that punitive tariffs
C
have hurt the overall economy of the region.
D
No error
E
B
32
No error
E
27
Although it is approximately 5 percent
Although it was first used
by news organizations to transmit photoB
A
graphs for publication in the 1920s,
fax machines did not come into widepread
D
C
use until nearly 60 years later. No error
E
B
33
Since the itinerary allotted very little time
A
for unexpected delays, our tour guide
insisted that we be at least 30 minutes early
B
C
for any scheduled train departure. No error
E
D
B
34
There is at least two oxygen tanks for each
A
B
climber at the base camp, although rarely
C
does anyone need more than one. No error
E
D
Because it is abundant and burns clean,
A
B
hydrogen is likely to become the preferred
C
energy source of the future. No error
D
E
GO ON TO THE NEXT PAGE Å Å Å
CHAPTER 14 / PRACTICE PSAT 1
371
that Hockney suggests. (12) Many art historians
also prefer to believe that van Eyck’s realism was
achieved through his skilled artistic eye, and not
some optical aid.
Directions for “Improving Paragraphs”
Questions
Below is an early draft of an essay. It requires
revision in many areas.
Line (1) Although many people consider science and
art to be very different fields of endeavor, they
came together in many surprising ways during
the Renaissance, which dawned in 15th-century
Europe. (2) One way was through the detailed
mechanical and anatomical drawings by brilliant
artists like Leonardo da Vinci. (3) According to
modern painter David Hockney, science and art
came together in yet another remarkable way
around 1425. (4) Even a casual analysis of
portraits of this era reveals a sudden and
dramatic increase in realism, which
Hockney thinks is best explained through
science.
(5) Whereas previous portraits were
characterized by awkwardness, artificiality and
formalism, the new portraits by artists like Jan
van Eyck and Robert Campin showed natural,
almost photorealistic expressions. (6) Hockney
suggests that the best explanation for the reason
about why such a dramatic shift in realism
occurred is because of the use of optical devices,
which caused them to become more realistic.
(7) Hockney believes that some artists of this era,
most notably van Eyck, used concave lenses for
projecting full-color images of his subjects on a
flat screen. (8) You can see how such a device
might work if you take a concave makeup mirror
on a sunny morning and angle it to reflect the
outside landscape onto your bathroom wall.
(9) The image is upside-down, but this was no
problem; artists could simply trace the image,
then invert the canvas and paint.
(10) Hockney’s theory is still very
controversial in the scientific and artistic
communities. (11) Many scientists argue that the
science of optics was not nearly well-developed
enough in the 15th century to support the
development of the sophisticated instruments
35
To improve clarity, which of the following
changes should be made to sentence 1?
(A)
(B)
(C)
(D)
(E)
B
36
they should be changed to these fields
which should be changed to of which
came should be changed to will have come
Although should be changed to Because
consider should be changed to consider that
Where is the best place to insert the sentence
below?
Another way is through the use of linear
perspective, as seen in the architectural drawings
of Michelangelo, Brunelleschi, and Rembrandt.
(A)
(B)
(C)
(D)
between sentences 1 and 2
between sentences 2 and 3
between sentences 3 and 4
before sentence 5, to begin the second
paragraph
(E) between sentences 5 and 6
B
37
Which of the following is the best version of
the underlined portion of sentence 6 (reproduced below)?
Hockney suggests that the best explanation for
the reason about why such a dramatic shift in
realism occurred is because of the artists’ use
of optical devices, which caused them to
become more realistic.
(A) (as it is now)
(B) it was because of optical devices why the
paintings of the artists became so much
more realistic
(C) because of optical devices was why these
artists’ pictures got more realistic
(D) these artists used optical devices to
produce dramatically more realistic
paintings
(E) the reason why these paintings had a
dramatic increase in realism is because
of the artists’ using optical devices
GO ON TO THE NEXT PAGE Å Å Å
Æ
Questions 35– 39 pertain to the
following passage.
B
z
The questions that follow ask you to make
improvements in sentence structure, diction,
organization, and development. Answering
the questions may require you to understand
the context of the passage as well as the
rules of standard written English.
5
372
B
38
Æ
z5
MC GRAW-HILL’S PSAT/NMSQT
Which of the following is the best version of
the underlined portion of sentence 7 (reproduced below)?
Hockney believes that some artists of this era,
most notably van Eyck, used concave lenses
for projecting full-color images of his subjects
on a flat screen.
(A) used concave lenses for the purpose of
projecting full-color images of his subjects onto flat screens
(B) used concave lenses to project his image
in full color on flat screens
(C) would have used concave lenses for projecting full-color images of their subjects
to a flat screen
(D) using concave lenses to project full-color
images of his subject onto a flat screen
(E) used concave lenses to project full-color
images of their subjects onto flat screens
B
39
Which of the following sentences would best
conclude the passage on a hopeful note while
maintaining the unity of the final paragraph?
(A) Arguments like this do not really help
artists to become better artists, so it is
best to leave such matters to the scientists that really care about them.
(B) The optical instruments that Hockney
suggests Renaissance artists used
wouldn’t be as difficult to make as many
people think.
(C) In the nineteenth century, many artistic
movements, like Impressionism, blossomed as a reaction against photorealism.
(D) Perhaps future artists will use even better
optical tools to create paintings that are
almost
indistinguishable
from
photographs.
(E) Although this controversy continues, it
has inspired scientists and artists alike
to revisit the art of the Renaissance,
and perhaps to appreciate anew the
mind of another age.
CHAPTER 14 / PRACTICE PSAT 1
373
ANSWER KEY
Section 1
Critical Reading
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
1. B
2. E
3. C
4. B
5. A
6. D
7. E
8. B
9. B
10. D
11. C
12. E
13. D
14. C
15. D
16. E
17. E
18. B
19. C
20. D
21. D
22. A
23. A
24. C
# Right (A):
————# Wrong (B):
————# (A) 2 14(B):
————-
Section 3
Critical Reading
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
25. B
26. C
27. A
28. C
29. A
30. D
31. E
32. D
33. C
34. E
35. D
36. C
37. B
38. D
39. E
40. A
41. B
42. C
43. A
44. C
45. A
46. B
47. E
48. D
# Right (A):
—————
# Wrong (B):
———–
# (A) 2 14(B):
————–
Section 2
Math
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
1. E
2. D
3. D
4. B
5. C
6. A
7. A
8. B
9. C
10. D
11. B
12. C
13. D
14. A
15. C
16. B
17. B
18. B
19. E
20. E
# Right (A):
————# Wrong (B):
————# (A) 2 14(B):
————-
Section 4
Math
A
A
A
A
A
A
A
A
21. B
22. C
23. B
24. E
25. E
26. A
27. D
28. C
# Right (A):
—————
# Wrong (B):
—————
# (A) 14 (B):
—————
A
A
A
A
A
A
A
A
A
A
29. 2/3 or .666 or .667
30. 16
31. 93
32. 18
33. 1212
34. 11
35. 4
36. 1/2 or .5
37. 9/14 or .642 or .643
38. 6/13 or .461 or .462
# Right (A):
————
Section 5
Writing
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
1. C
2. B
3. E
4. C
5. D
6. A
7. E
8. C
9. A
10. E
11. C
12. B
13. B
14. C
15. D
16. A
17. C
18. B
19. E
20. D
21. B
22. D
23. C
24. D
25. B
26. E
27. A
28. B
29. B
30. E
31. B
32. C
33. E
34. A
35. A
36. B
37. D
38. E
39. E
# Right (A):
————# Wrong (B):
————# (A) 2 14(B):
————
374
MC GRAW-HILL’S PSAT/NMSQT
SCORE CONVERSION TABLE
How to score your test
Use the answer key on the previous page to determine your raw score on each section. Your raw score on any
section is equal to the number of correct answers on that section minus 1/4 of the number of wrong answers,
with the exception of the mathematical “grid-in” section, on which wrong answers are not deducted from
your score. Remember to add the raw scores from Sections 1 and 3 to get your Critical Reading raw score,
and to add the raw scores from Sections 2 and 4 to get your Math raw score. Write the three raw scores here:
Raw Critical Reading score (Section 1 þ Section 3): ____________
Raw Math score (Section 2 þ Section 4): ____________
Raw Writing score (Section 5): ____________
Use the table below to convert these to scaled scores.
Scaled scores:
Raw
Score
Critical
Reading
Scaled
Score
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
80
80
78
76
74
72
71
69
68
67
66
64
63
62
62
61
60
59
58
57
56
55
54
54
54
52
51
50
Critical Reading: ____________
Math
Scaled
Score
80
77
74
72
70
68
66
65
64
62
61
60
59
58
57
55
54
53
Writing
Scaled
Score
80
80
78
77
76
74
73
71
69
68
66
65
63
62
60
59
57
56
55
Math: ____________
Writing: ____________
Raw
Score
Critical
Reading
Scaled
Score
Math
Scaled
Score
Writing
Scaled
Score
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
21
22
23
24
25
26
27 or less
49
48
47
46
45
44
43
42
41
40
39
38
37
36
34
33
32
30
29
27
25
22
20
20
20
20
20
20
52
51
50
48
47
46
45
44
43
42
41
40
39
38
36
35
34
32
30
29
26
23
20
20
20
20
20
20
54
52
51
50
49
48
46
45
44
43
41
40
39
37
36
35
33
32
31
30
29
28
27
25
24
22
21
20
CHAPTER 14 / PRACTICE PSAT 1
375
Detailed Answer Key
Section 1
1. B
If the remark was only seemingly offhand,
then it must have actually been deliberate.
celebrated ¼ famous; calculated ¼ planned for deliberate effect; reflexive ¼ automatic; conventional ¼
conforming to custom
2. E
The term symbiosis refers to a situation in
which different species act in a mutually beneficial
way to one another. parasitism ¼ relationship in
which one organism harms another by taking advantage of it; precarious ¼ dangerous; antagonism ¼
hostility; beneficial ¼ helpful
3. C
A career to which one feels called is a vocation, which derives from the Latin vocare, to call.
embodiment ¼ a representation in bodily form;
acquisition ¼ something acquired; corollary ¼ a
logical deduction
4. B
The word although indicates a contrast
between the fact that the value of liberty is timeless
and the fact that our appreciation of it is not. The
first word, logically, should be a synonym of value
and the second a synonym of temporary.
benevolence ¼ kindness;
fleeting ¼ short-lived;
anachronisms ¼ things that are out of place in time;
transitory ¼ temporary; diversions ¼ entertainments;
ephemeral ¼ short-lived
5. A
This sentence contains a reiteration or definition. The missing word means unexpected
changes.
vicissitudes ¼ unexpected
changes;
veneers ¼ superficial pretenses or outward shows;
evanescence ¼ quality of being able to vanish quickly
6. D
The words by and thereby indicate logical
cause-and-effect relationships within the sentence.
Use your common sense to complete the sentence
in a logical way. What would one expect a change
in global climate to do to our ancestors in trees,
and what would one expect to happen to human evolution as a result of this? A change in climate would
produce a change in food availability, encouraging
our ancestors to climb out of the trees and to
evolve. hasten ¼ to cause to occur more quickly;
resolve ¼ solve a problem; spur ¼ encourage;
impel ¼ force; propel ¼ to push forward
7. E
If a Senator chose to affiliate himself with the
opposition, he would have abandoned his own party,
which would likely have treated him as a traitor.
repudiate ¼ to reject the validity of; curator ¼
director of a museum; recluse ¼ hermit; ascertain ¼
determine the truth of; complement ¼ something
that, when added to something else, forms a whole;
expatriate ¼ one who lives in a country other than
his or her native land; forsake ¼ abandon; apostate ¼
one who abandons one’s party or faith
8. B
If a dictator could not be assuaged (pacified),
and issued bellicose (war-mongering) announcements, then it would seem almost impossible to
avoid conflict. diplomacy ¼ attempts at peaceful conciliation;
disclosed ¼ revealed;
conciliation ¼
appeasement; averted ¼ prevented; tact ¼ the ability
to appreciate the delicacy of a situation and act
appropriately; denigrated ¼ defamed, disparaged;
belligerence ¼ antagonism, pugnaciousness; forestalled ¼ delayed; jingoism ¼ excessive and aggressive nationalism; circumvented ¼ overcame through
clever maneuvering
9. B
The author states that students [come] to us
from the best high schools in America (lines 10 –11).
This suggests that the author is a college professor.
10. D
The top of the pyramid (as opposed to the
rest of the pyramid) is described as the place where
the most profound questions of our era are examined
(lines 35– 36).
11. C
The author of Passage 1 states that there
seems to be no grounding (lines 17–18) in the fundamental academic skills for college students, but
suggests, through the ladder metaphor, that there
should be. The author of Passage 2, however,
claims that we are losing too many students in building the pyramid (of fundamental skills) (lines 37 –38).
12. E
The author of Passage 1 uses the ladder as a
metaphor for academic learning, and the author of
Passage 2 uses the pyramid as a metaphor.
13. D
The author of Passage 1 states that he is
writing at the end of a brief introduction (lines 7 –8)
and that he is regarding most of the criticism and
much of Fitzgerald’s work (lines 1–2). Therefore, he
suggests that he is writing an introduction to a
book of criticism.
376
14. C
The author explains that in saying that
modern criticism. . . is. . . too refined (lines 12 –13), he
means that critics tend to make too much of small
things (lines 14 –15).
15. D
The author states that there is joy in Fitzgerald’s work that should not be passed over (lines 20 –21)
and that Edmund Wilson, in particular, recognized
this quality in Fitzgerald’s work.
16. E
In saying that a writer. . . is commonly
charged with having too narrow a range (lines 29–
31), he is saying that the writer is accused of
dealing only with a short list of themes.
17. E The author suggests that examining Fitzgerald’s original manuscripts, which contain strikeovers,
and pencillings, and second and third thoughts (lines
46 –47), can help a writer to appreciate that good
writing involves a good deal of reworking.
18. B
The fifth paragraph of Passage 1 expresses a
concern that some Fitzgerald scholarship is solemn
and heavy (line 51), after expressing in a previous
paragraph that Fitzgerald’s work is filled with joy
(line 20). He also suggests that there should be some
licensing procedure that would prevent bad writers. . .
from dealing with Fitzgerald (lines 52 –55). He is
therefore showing a concern about the quality and
tone of Fitzgerald scholarship.
19. C
The following sentence goes on to explain
that, in his earliest works, Fitzgerald’s optimistic
sense of the value of experience is overshadowed by a
personal intuition of tragedy (lines 83 –86). In other
words, Fitzgerald’s novels contain tragic elements.
20. D
This final paragraph contrasts those who
possess the necessary means (line 107), that is, the
wealthy, with the disinherited (line 110), that is, the
poor. When the author states that the disinherited
[are] forever barred from the white palace (lines 110–
111), he means that they do not have access to the
wealth and privilege of the affluent.
21. D
The author of Passage 1 would strongly disagree because he states, in lines 63 –64, that Fitzgerald will probably continue to claim the interest of
both the general reader and the scholar-critic.
22. A
The joy mentioned in line 20 of Passage 1 is
described as a feature of Fitzgerald’s work that
should not be passed over (line 21) and as something
that is exceedingly rare (line 24) and has worth (line
28), but the wonder described in line 86 of Passage
MC GRAW-HILL’S PSAT/NMSQT
2 is a feature of Fitzgerald’s work that, the author
of Passage 2 claims, is chastened by satiric and
ironic insights (line 87). In other words, the author
of Passage 1 considers this quality to be a unique
and worthy feature of Fitzgerald’s work, while the
author of Passage 2 considers it to be compromised
by intimations of tragedy.
23. A
The author of Passage 1 suggests that some
criticism dwells upon profundities, complexities, and
tragic implications (lines 21 –23) in Fitzgerald’s
work. The author of Passage 2 states that Fitzgerald’s
works have been labeled. . . by their most recent critics,
as darkly pessimistic studies (lines 74 –75).
24. C
The author of Passage 1 states in the third
paragraph, as well as in the fifth, that critics dwell
excessively on profundities, complexities, and tragic
implications (lines 22 –23) in Fitzgerald’s works, and
that too much scholarship on Fitzgerald has become
solemn and heavy (line 51). He emphasizes
Fitzgerald’s extraordinary felicity of expression (line
62) and suggests that good criticism of Fitzgerald
should be likewise felicitous, not heavy and tragic.
Section 2
1. E The area of a rectangle is given by the formula
A ¼ bh, and the area of a triangle is given by the
formula A ¼ 12bh. So the rectangle has an area of
(4)(6) ¼ 24, and the triangle has an area of
1
2(4)(4) ¼ 8. So the area of the rectangle is 3
times the area of the triangle.
(Chapter 11 Lesson 5: Areas and Perimeters)
2. D
The algebraic method:
Multiply by 6:
x ¼ 2y þ 2
6x ¼ 12y þ 12
This equation states that 6x is 12 more than 12y.
(Don’t forget to distribute the multiplication on the
right-hand side!)
Although the algebraic method is the simplest, and
should be easy to understand, you can also solve
this by simply choosing values for x and y that work
in the original equation. For instance, if x ¼ 2y þ 2,
then x could be 4 and y could be 1, because
4 ¼ 2(1) þ 2. The question how much greater is 6x
than 12y now becomes how much geater is 6(4) than
12(1) or how much greater is 24 than 12? The
answer is clearly 24 2 12 ¼ 12.
(Chapter 9 Lesson 1: Solving Equations)
(Chapter 9 Lesson 2: Systems)
(Chapter 8 Lesson 2: The Laws of Arithmetic)
CHAPTER 14 / PRACTICE PSAT 1
377
3. D
First, notice that any number that is divisible
by 6 must necessarily be divisible by 2 also, since
6 ¼ (3)(2). Therefore, the question is simply asking:
how many multiples of 6 are there between 10 and
40? The answer choices quickly tell you that the
answer can be no more than 6, so it’s easy enough
to list them: 12, 18, 24, 30, 36.
(Chapter 8 Lesson 7: Divisibility)
4. B
First notice that 100 hours is a little bit more
than 4 days, because 100 hours (1 day/24
hours) ¼ 4 1/6 days, or 4 days and 4 hours. Since
4 days later it will be 4:30 p.m. again, in 4 days and
4 hours it will be 8:30 p.m.
(Chapter 7 Reasoning Skill 3: Finding Patterns)
5. C To use the algebraic method, start by defining
d as the number of candy bars that Denise sold (since
this is what the question is asking for). If Emily sold
four times as many candy bars as Denise, then Emily
sold 4d candy bars. If Denise sold 3 times as many as
Carrie, then Carrie sold 13 d candy bars. Since they
sold 48 altogether,
d þ 4d þ 13 d ¼ 48
Simplify:
Multiply by 3=16:
(16=3)d ¼ 48
d ¼9
x
(2 x)
(A) x ¼ 0:5
þ
þ
þ
(B) x ¼ 0
0
þ
0
(C) x ¼ 0:5
þ
(D) x ¼ 1:5
þ
(E) x ¼ 2:5
þ
(Chapter 9 Lesson 5: Factoring)
(Chapter 10 Lesson 1: New Symbol or Term
Problems)
8. B
You might start by noticing that the line contains the points (0, 3) and (6, 0). Remember that the
slope of the line is simply the “rise” between two
points divided by the “run” between those same two
points. If you walk from (0, 3) to (6, 0), your “run”
would be 6 2 0 ¼ 6, and your “rise” would be
0 2 3 ¼ 23. Therefore the slope of this line is
23/6 ¼ 21/2. Now look at the choices. Notice that
all of the equations are in the form y ¼ mx þ b, and
in this form m stands for the slope, and b stands for
the y-intercept. Since the y-intercept is clearly 3, the
correct equation is (B).
Alternatively, you can just “plug in” the points (0, 3)
and (6, 0) to the equations, and eliminate any
equations that aren’t true for both points. For
instance:
Plug in (0, 3)
Alternatively, you can simply “test” the answer
choices and work by process of elimination. Remember that if you “work backward” like this, you should
always start with the middle value, which is almost
always at (C). You would simply check whether, if
Denise sold 9 candy bars, the total would come out
to 48. It does, because Emily would have sold
(4)(9) ¼ 36, and Carrie would have sold 13(9) ¼ 3,
and 9 þ 36 þ 3 ¼ 48.
(Chapter 9 Lesson 7: Word Problems)
6. A
Remember that a straight angle has a
measure of 1808. Therefore
Simplify:
Divide by 5:
2x þ 3x ¼ 180
5x ¼ 180
x ¼ 36
Since the y8 angle is “vertical” with the 2x8 angle, the
two must be congruent, so y ¼ 2x ¼ 2(36) ¼ 72.
(Chapter 11 Lesson 1: Lines and Angles)
7. A
The brute force method is to simply evaluate
2x 2 x 2 for each of the “input” values until you get a
positive result. It’s a bit easier, though, to simply
factor the expression and pay attention to the signs
of the factors. First, factor the function expression:
f (x) ¼ 2x 2 x 2 ¼ x(2 2 x). Now check the signs:
x(2 x)
Plug in (6, 0)
(A) 3 ¼ 2(0) þ 3
(Yes) 0 ¼ 2(6) þ 3 (No)
(B) 3 ¼ 1=2(0) þ 3 (Yes) 0 ¼ 1=2(6) þ 3 (Yes)
(C) 3 ¼ 1=2(0) þ 6 (No) 0 ¼ 1=2(6) þ 6 (No)
(D) 3 ¼ 1=2(0) þ 3
(Yes) 0 ¼ 1=2(6) þ 3 (No)
(E) 3 ¼ 2(0) þ 6
(No) 0 ¼ 2(6) þ 6 (No)
(Chapter 11 Lesson 4: Coordinate Geometry)
9. C
You can use simple algebra or plug in a value
for b, whichever is easier. If g is the total number of
girls in the class, and “the number of girls is 6 less
than twice the number of boys,” then g ¼ 2b 2 6.
The total number of students in the class, therefore,
is b þ g ¼ b þ (2b 2 6) ¼ 3b 2 6. But if 2 girls are
absent, the number of students present is
3b 2 6 2 2 ¼ 3b 2 8.
Alternatively, you could just pick a simple value for b,
like 10. If the number of girls is 6 less than twice the
number of boys, then there are 20 2 6 ¼ 14 girls, for a
total of 10 þ 14 ¼ 24 students. If 2 are absent, there
must be 22 present. Notice that choice (C) is the only
one that gives a value of 22 when you plug in 10 for b.
(Chapter 9 Lesson 7: Word Problems)
10. D
Take the square root:
Subtract 5:
(x þ 5)2 ¼ 0
(x þ 5) ¼ 0
x ¼ 5
378
MC GRAW-HILL’S PSAT/NMSQT
Therefore
(x 2 1)(x þ 1) ¼ (25
21)(25 þ 1) ¼
(26)(24) ¼ 24
(Chapter 10 Lesson 3: Numerical Reasoning
Problems)
11. B
Be sure to mark up the diagram with the
information you are given and the information you
can deduce:
A
l
4
3
B
5
C
Remember that the formula for the circumference of
a circle is c ¼ 2pr. Since the circumference of the
circle is 6p,
6p ¼ 2p r
Divide by2p:
3¼r
Also, recall that any tangent to a circle is perpendicular to the radius that touches the point of tangency.
Therefore, D ABC is a right triangle with legs of 3
and 4. To find BC, the hypotenuse, you might
notice that this is the common 3-4-5 triangle, or
you can simply use the Pythagorean theorem:
32 þ 42 ¼ (BC)2
Simplify:
25 ¼ (BC)2
Take the square root:
5 ¼ BC
(Chapter 11 Lesson 8: Circles)
(Chapter 11 Lesson 3: The Pythagorean Theorem)
12. C
Since the integers are consecutive and their
sum is 210, you might be able to find them simply by
guessing and checking. Or if you prefer, you can find
them algebraically. Just call the least of the integers
x. Then, the statement that the five consecutive integers have a sum of 210 becomes
x þ (x þ 1) þ (x þ 2) þ (x þ 3) þ (x þ 4)
Simplify:
5x þ 10
Subtract 10:
5x
Divide by 5:
x
¼ 10
¼ 10
¼ 20
¼ 4
Therefore the five numbers are 24, 23, 22, 21, and
0. Now you are to find the greatest possible product of
three of these numbers. All the numbers are negative
except 0. The product of any three negatives is always
negative, but the product of any number and 0 is
always 0. Therefore, the greatest product you can
get by multiplying three of these numbers is 0.
(Chapter 10 Lesson 3: Numerical Reasoning
Problems)
13. D
Just focus on the Wednesdays. Since the
first of the month is a Monday, the first Wednesday
must be the 3rd. Since Wednesdays happen to occur
every 7 days, the other Wednesdays are on the 10th,
17th, and 24th. (There is no 31st because there are
only 30 days.) Therefore 4 of the 30 days are
Wednesdays, so the probability is 4/30 ¼ .1333. . .
(Chapter 10 Lesson 3: Numerical Reasoning Problems)
(Chapter 7 Reasoning Skill 3: Finding Patterns)
14. A
Remember that jxj means the distance from
x to 0 on the number line. So if jxj . 2, then either
x . 2 or x , 22. (Think about it.) So two simple possible values of x are 3 and 23. If x can be 23, then
statements I and III are not necessarily true since
23 . 0 is not true and (23)3 . 2 is not true. If you
eliminate every answer choice that contains statement I or statement III, you are left only with (A).
Statement II must be true because if you square
both sides of jxj . 2, you get x 2 . 4, and if x 2 is
greater than 4, it must certainly also be greater
than 2.
(Chapter 9 Lesson 6: Inequalities, Absolute Values,
and Plugging In)
15. C Since marbles only come in whole numbers,
if the number of red marbles is 5/6 the number of
white marbles, then the number of red marbles
must be a multiple of 5. (Just think of the ways it
could happen: 5 red and 6 white, 10 red and 12
white, etc.) Likewise, if the number of red marbles
is 6/7 the number of blue marbles, then the
number of red marbles must also be a multiple of
6. Since the smallest multiple of 5 and 6 is 30, this
is the least possible number of red marbles. Since
the number of red marbles is 5/6 the number of
white marbles,
30 ¼ (5=6)w
Multiply by 6=5:
36 ¼ w
Since the number of red marbles is 6/7 the number of
blue marbles,
30 ¼ (6=7)b
Multiply by 7=6:
35 ¼ b
So the least possible total number of marbles is
30 þ 36 þ 35 ¼ 101.
(Chapter 8 Lesson 3: Fractions)
(Chapter 8 Lesson 4: Ratios and Proportions)
16. B
A sequence in which each term is equal to
the previous term times a constant (a fixed number)
is called a geometric sequence. The number you
must multiply each time is the common ratio, b/a,
which is also equal to a/8 and 27/b. You might
simply test the answer choices, starting with (C), to
see how the sequence works out. For instance,
testing (C) 3.375 means multiplying the first term,
CHAPTER 14 / PRACTICE PSAT 1
8, by 3.375 to get the next term, and so on. This
gives you
379
of y. Since we assumed that x ¼ 1,
x2 þ 1=x2 ¼ (1)2 þ 1=(1)2 ¼ 2
8, 27, 91:125, 307:55
but this doesn’t work, because the fourth term should
be 27. Therefore, 3.375 is too big, and so we can eliminate (C), (D), and (E). Next, try choice (B). Multiplying by 1.5 each time works perfectly:
8, 12, 18, 27
So the answer is (B).
(Chapter 7 Reasoning Skill 3: Finding Patterns)
17. B
You should be able to sketch a quick graph
of this line using one of two methods. The first way
is to use the fact that, when a linear equation is
in the form y ¼ mx þ b, the slope is m and the
y-intercept is b. So the slope of this line is 2/3 and
its y-intercept is 1. First plot a point at the y-intercept.
Then move up 2 and right 3 and plot a second point.
Then connect the points:
Therefore, we want to know which choice has a value
of 2 when we plug in y ¼ 2. Evaluate each choice:
(A)
(B)
(C)
(D)
(E)
y2 þ 2 ¼
y2 þ 1 ¼
¼
y2
y2 1 ¼
y2 2 ¼
(2)2 þ 2 ¼
(2)2 þ 1 ¼
(2)2
¼
(2)2 1 ¼
(2)2 2 ¼
6
5
4
3
2
Clearly, only choice (E) gives the value we want: 2.
You can also solve this problem algebraically:
(x þ 1=x)
Square both sides: (x þ 1=x)(x þ 1=x)
FOIL:
x2 þ x=x þ x=x þ 1=x2
Simplify:
x2 þ 1 þ 1 þ 1=x2
Simplify:
x2 þ 2 þ 1=x2
Subtract 2:
x2 þ 1=x2
¼y
¼ y2
¼ y2
¼ y2
¼ y2
¼ y2 2
(Chapter 9 Lesson 6: Inequalities, Absolute Values,
and Plugging In)
(Chapter 9 Lesson 1: Solving Equations)
20. E
Be sure to mark up the diagram with any
given information and any information you can
deduce:
The other simple method is to choose easy values for
x, like 0 and 3, and plug these into the equation to get
the corresponding values of y. Just as in the previous
method, this will give you the points (0, 1) and (3, 3).
Now simply plot the points in the choices and notice
that only choice (B) (1, 1) is below the line.
(Chapter 11 Lesson 4: Coordinate Geometry)
18. B First you must notice that 27 is a power of 3:
33 ¼ 27. Use this to make a substitution: 3n21 ¼ 2721
Substitute 33 for 27:
3n1 ¼ (33 )1
Simplify:
3n1 ¼ 33
Equate the powers:
n 1 ¼ 3
Add 1:
n ¼ 2
First, since the slope of the line is 2 and the line
passes through (0, 0), it must also pass through (6,
12). (Remember slope ¼ rise/run ¼ 12/6 ¼ 2.) So,
label the top right corner of the rectangle (6, 12).
Next, notice that the two shaded right triangles
must be similar, because all of their corresponding
angles are congruent by the parallel lines theorem.
Therefore all of the corresponding sides are
proportional:
m 12
¼
6
10
(Chapter 9 Lesson 3: Working with Exponents)
19. E
You can do this algebraically or by plugging
in. Here, perhaps plugging in is easier. Notice that if
you plug in x ¼ 1, you get y ¼ 1 þ 1/1 ¼ 2. Now, the
question asks for the value of x 2 þ 1/x 2 in terms
Multiply by 6:
Therefore, the
12 þ 7.2 ¼ 19.2
y-coordinate
m ¼ 7:2
of
point
A
is
380
(Chapter 11 Lesson 1: Lines and Angles)
(Chapter 11 Lesson 4: Coordinate Geometry)
(Chapter 11 Lesson 6: Similar Figures)
Section 3
25. B
If Harold is unlike other farmers, then he
thinks of rain as something contrasting a benefit.
hardship ¼ a trying situation
26. C
A perfectionist is one who cannot accept
flaws in his or her work. Therefore, the tendency to
destroy works that are less than perfect would be a
hallmark
of
perfectionism.
paragon ¼ prime
example; mediocre ¼ of average quality; proponent ¼
supporter, advocate; aesthetic ¼ relating to a sense of
the beautiful; advocate ¼ one who speaks out for a
cause; monetary ¼ pertaining to money
27. A
Clearly, Joseph has the tendency to pick
fights. belligerence ¼ eagerness to fight; diligence ¼
persistent application to one’s work; fortitude ¼
strength; restraint ¼ ability to control one’s urges;
eloquence ¼ ability to speak fluently and persuasively
28. C
Discounted merchandise and free gift wrapping are things that are likely to appeal to shoppers.
If the shoppers were angry, such offers seem to be
attempts to appease their anger. exculpate ¼ free
from blame; impede ¼ hinder the progress of;
mollify ¼ appease, soothe the anger of; pilfer ¼ steal;
abridge ¼ to shorten the length of a written work
29. A
Severe immigration restrictions would logically render a country less vulnerable to foreign terrorists, but would also hinder the influx (inward flow) of
creative ideas. pervious ¼ penetrable; stem ¼ stop
the flow of; impregnable ¼ incapable of being penetrated; hasten ¼ to cause to happen sooner;
potent ¼ strong
30. D
This passage compares and contrasts two
kinds of evidence (lines 5– 6) in history: oral traditions
and archaeology (lines 4– 5).
31. E
The nonmaterial world of ideas, values and
beliefs (lines 15 –16) is said to be provided by oral
sources (line 14). This nonmaterial world, according
to the passage, is worthy of study but only ascertainable through oral traditions.
32. D The overall purpose of the passage is to criticize irrationality. The first sentence characterizes
the irrational tidal waves of the last big war (lines 2 –
3) as causing agony and despair. It then goes on to
bemoan the fact that man is not rational enough
MC GRAW-HILL’S PSAT/NMSQT
(lines 12 –13) to take advantage of recent advancements and that reality does not conform to our
rational prescriptions (line 22).
33. C
The parenthetical comment states that the
poor might have most reason for such reactions (as
unrest and violence). In other words, the poor are
the most justified in acting rebelliously.
34. E
The author states I go off down to the river to
get my strength back (lines 28–29). In other words, the
river rejuvenates him.
35. D
The author states that without that “everything,” I can’t get along either. The “everything” that
he is referring to is the traffic (line 4), which he says
gets on his nerves, and the people and things (lines
16 –17) that he encounters every day. In other
words, he needs these things, but occasionally
needs to get away from them also.
36. C
The thing that we haven’t managed to pull
out of our dusty old dictionaries (lines 27 –28) is the
recreation (line 22) or the rest [that helps one to get
one’s] strength back regularly (line 26), in other
words, something that helps to restore one’s
strength.
37. B
The constant flight from open conflict (lines
66–67) is the escape from or fleeing from conflict.
38. D
The author states that work has lost its original meaning long since its primeval, ennobling, creative function (lines 72 –73). In other words, long ago
work was meant as a creative endeavor, and it has
lost its meaning as such.
39. E
This paragraph describes how the author’s
appointment with the river has expired (lines 83 –84)
because the city is waking up (line 82) behind him.
The pensioners (line 90) are mentioned as examples
of those people and things that are intruding on his
solitude at the river.
40. A
The passage as a whole describes the conflict that the narrator feels between his need for
people and things (lines 16–17) and the tendency of
these things to occasionally get [him] down (line
17), whereupon he seeks solitude and rejuvenation
at the river. Therefore, the main conflict is between
solitude and sociability.
41. B
The first line of the passage states that
according to Kant, his reading of David Hume awakened him from his dogmatic slumber and set him on
CHAPTER 14 / PRACTICE PSAT 1
the road to becoming the “critical philosopher” (lines
1 –4). In other words, Hume’s writings inspired
Kant in his philosophical thinking.
42. C
The term dogmatic means very rigid
and preachy in one’s views. By saying that he was
awakened. . . from his dogmatic slumber (lines 2– 3),
the author is stating that Kant was far more rigid in
his thinking before reading the work of David Hume.
43. A The passage states that the theme (line 35) of
the “Transcendental Dialectic” is this inevitable
failure (lines 35) of all theoretical attempts to know
things-in-themselves (lines 33 –34).
44. C
According to the passage, in Critique of Pure
Reason, Kant shows the necessity of a belief in [the
existence of God, freedom, and immortality] in his
moral philosophy (lines 43 –45). In other words,
Kant’s moral system required the belief in free will.
45. A
According to the passage, Kant’s categorical
imperative (lines 46–47) is to “Act as if the maxim from
which you act were to become through your will a universal law“ (lines 47 –49). In other words, act as if the
principles behind your acts were the principles that
everyone used; that is, they applied to all human
beings.
46. B
The author states that, according to Kant,
we do not act infallibly in accordance with [the categorical imperative] (lines 53 –54) because we almost
always act according to inclination (lines 55–56);
that is, we do what our subjective needs and desires
compel us to do. Another way of saying this is that
our acts are necessarily subjectively contingent (line
58), that is, we can only act according to our “subjective” needs and desires, so we cannot do infallibly
what is objectively necessary (line 57).
47. E
The bridge (line 73) is one between the sensible and the intelligible worlds (line 69), so it is a bridge
between what can be sensed and what can be
understood.
48. D
The final paragraph describes what Kant
went on to state in Critique of Practical Reason.
It then summarizes another later work of Kant, the
Critique of Judgment.
Section 4
21. B
A square with perimeter of 20 centimeters
must have sides of length 20 4 4 ¼ 5 centimeters.
381
Since the area for a square is given by the formula
A ¼ s 2, the area of the square is 52 ¼ 25 square centimeters, and one-half of 25 is 12.5.
(Chapter 11 Lesson 5: Areas and Perimeters)
22. C
You can solve this one algebraically or by
simply testing the choices. To solve algebraically,
translate into an equation. If the number is equal to
1/3 of its square,
Multiply by 3:
Subtract 3x:
Factor:
Use the 0 product property:
x
3x
0
0
x
¼ (1=3)x2
¼ x2
¼ x2 3x
¼ x(x 3)
¼ 0 or x ¼ 3
Since 0 is not among the choices, the answer must be
(C) 3.
Alternatively, you can simply test the choices, taking
one-third of the square of each number until you get
a result that equals the original number. Of course,
that works with 3 because 3 ¼ (1/3)(32).
(Chapter 9 Lesson 1: Solving Equations)
23. B
This one is probably most easily solved
algebraically. Since each pile has k more checkers
than the previous pile and the first pile has 3 checkers, the piles have 3, 3 þ k, 3 þ 2k, and 3 þ 3k checkers, respectively. Since the total number of checkers
is 30,
Simplify:
Subtract 12:
Divide by 6:
3 þ (3 þ k) þ (3 þ 2k) þ (3 þ 3k)
12 þ 6k
6k
k
¼ 30
¼ 30
¼ 18
¼3
(Chapter 9 Lesson 7: Word Problems)
24. E
If a number is equal to 3/5 of itself plus 240,
Subtract (3=5)x:
Multiply by 5=2:
x ¼ (3=5)x þ 240
(2=5)x ¼ 240
x ¼ 600
(Chapter 9 Lesson 1: Solving Equations)
(Chapter 9 Lesson 7: Word Problems)
25. E
The total number of books sold (in thousands) is 500 þ 325 þ 375 ¼ 1,200. Since 500 nonfiction books have been sold, and x corresponds to the
central angle of the sector representing nonfiction
382
MC GRAW-HILL’S PSAT/NMSQT
books, you can set up a proportion:
Cross-multiply:
Divide by 1,200:
500
x
Part
¼
¼
360
Whole 1,200
180,000 ¼ 1,200x
150 ¼ x
(Chapter 8 Lesson 4: Ratios and Proportions)
26. A
It’s helpful to know that if a set of numbers
is evenly spaced, its median always equals its average
(arithmetic mean). Since 10 consecutive even integers are certainly evenly spaced, statement I must
be true. [This eliminates choice (B).] To check statements II and III, you should take a closer look at set
S. You can find the 10 numbers fairly easily by using
what we just deduced, namely, that 23 must be the
median, and so it splits the set in half. Therefore set
S must consist of the five even integers just before
23 and the five even integers just after 23:
14, 16, 18, 20, 22, 24, 26, 28, 30; and 32
Clearly the difference between 32 and 14 is greater
than 10, so statement II is not true. Also, set S contains two multiples of 5: 20 and 30. Therefore, statement III is not true, and the answer is (A).
(Chapter 10 Lesson 2: Mean/Median/Mode
Problems)
27. D
2
2k
(2n )(2k ) ¼ 2
2nþk ¼ 21
n þ k¼ 1
2n ¼
Multiply by 2k :
Simplify:
Equate exponents:
(Chapter 9 Lesson 3: Working with Exponents)
28. C
Since the area of the square basepisffiffiffiffiffiffiffiffi
144, the
length of one side of the square must be 144 ¼ 12.
This is also the base of one of the triangular faces.
Let’s call the height of this triangular face h. Notice
that h is also the hypotenuse of a right triangle with
legs of 6 and 8. (One leg is the height of the
pyramid, which we know is 8, and the other leg is
half the length of the side of the square.)
Next, notice that this right triangle is simply a multiple of a 3-4-5 triangle, so its sides have length 6-810. Alternatively, you can use the Pythagorean
theorem to find h:
Simplify:
Simplify:
Take the square root:
62 þ 82
36 þ 64
100
10
¼ h2
¼ h2
¼ h2
¼h
Thus the triangular face has a base of 12 and a height
of 10, so its area is (1/2)(12)(10) ¼ 60 square inches.
(Chapter 11 Lesson 3: The Pythagorean Theorem)
(Chapter 11 Lesson 5: Areas and Perimeters)
(Chapter 11 Lesson 7: Volumes and 3-D Geometry)
29. 2/3 or .666 or .667
1/4 of 80 is (1/4)(80) ¼ 20 and 1/3 of 90 is (1/
3)(90) ¼ 30. 20 4 30 ¼ 2/3 or .666. . .
(Chapter 8 Lesson 1: Numbers and Operations)
30. 16
Using the definition, 5 ø 3 ¼ (5 þ 3)(5 2 3) ¼
(8)(2) ¼ 16.
(Chapter 7 Reasoning Skill 1: Finding Patterns)
31. 93
Recall that the sum of the angles in a quadrilateral is always 3608, because a diagonal divides
the quadrilateral into two triangles with 1808 each.
Therefore
x þ x þ x þ y ¼ 360
Substitute:
89 þ 89 þ 89 þ y ¼ 360
Simplify:
267 þ y ¼ 360
Subtract 267:
y ¼ 93
(Chapter 11 Lesson 2: Triangles)
32. 18 We know that, for some value of x, f (x) ¼ 6,
and this is the largest possible output of the function.
Let’s say that the value of x for which this is true is 1,
so that f (1) ¼ 6. Now we are asked to find the greatest
possible value of 3f(x 2 1). Notice that if we substitute x ¼ 2, we get 3f (2 2 1) ¼ 3f (1) ¼ 3(6) ¼ 18.
Since the value of f (x) can be no greater than 6, this
must be the greatest possible value of 3f (x 2 1).
(Chapter 10 Lesson 1: New Symbol or Term
Problems)
33. 1,212 It is convenient to know that if a number
is divisible by 3, the sum of its digits will also be a
multiple of 3. Likewise, if a number is divisible by
9, the sum of its digits will also be a multiple of
9. (Don’t generalize this to any other factors,
though; this is only true for numbers divisible by 3
or 9. For instance, the sum of the digits of a multiple
of 5, like 25, is NOT necessarily a multiple of 5.)
Therefore, we know that 4 þ A þ 3 ¼ 7 þ A is a
CHAPTER 14 / PRACTICE PSAT 1
383
multiple of 3. The largest A could be, then, is 8,
because 7 þ 8 ¼ 15 is a multiple of 3. Also,
7 þ B þ 9 ¼ 16 þ B is a multiple of 9, so the largest
B could be is 2, since 16 þ 2 ¼ 18 is a multiple of
9. (Remember that A and B represent single digits.)
Therefore, the greatest that m þ n could be is
483 þ 729 ¼ 1,212.
(Chapter 8 Lesson 7: Divisibility)
34. 11
Write 8 as a power of 2:
Simplify:
Equate the exponents:
Subtract 1:
2mþ1
2mþ1
2mþ1
mþ1
m
¼ 84
¼ (23 )4
¼ 212
¼ 12
¼ 11
(Chapter 9 Lesson 3: Working with Exponents)
35. 4 If the product of four numbers is 0, then one
of the numbers must be 0. If the median of the
numbers is 3.5, then two of the numbers must be
greater than 3.5, and two of the numbers must be
less than 3.5. So, in increasing order, the numbers
are 0, n, 5, 9. Since the median is the average of the
two middle numbers,
Multiply by 2:
Subtract 5:
(n þ 5)=2 ¼ 3:5
nþ5 ¼7
n ¼2
So the average (arithmetic mean) of the four
numbers is (0 þ 2 þ 5 þ 9)/4 ¼ 16/4 ¼ 4.
(Chapter 10 Lesson 2: Mean/Median/Mode
Problems)
36. 1/2 or .5 Notice first that the height of the rectangle is 6. The area of a rectangle is given by the
formula A ¼ bh, so if the area of the rectangle is 90,
then
90 ¼ 6b
Divide by 6:
15 ¼ b
So the base is 15. Write this into the diagram. The distance from O to P is 3, so the other part of the base is
15 2 3 ¼ 12. The slope of line PQ is the “rise” divided
by the “run,” which is 6/12 ¼ 1/2. Also, you can use
the slope formula slope ¼ (y2 2 y1)/(x2 2 x1) with the
two points on the line (3, 0) and (15, 6): (6 2 0)/
(15 2 3) ¼ 6/12 ¼ 1/2.
(Chapter 11 Lesson 6: Similar Figures)
37. 9/14 or .642 or .643 The phrase at this rate indicates that you can set up a proportion of equivalent
rates:
2
tank
x tank
7
¼
1
3 hours
1 hours
3
2
tank
x tank
¼
Simplify mixed number: 7
4
3 hours
hours
3
Cross-multiply:
Simplify:
Multiply by 21:
Divide by 28:
Simplify:
2
4
(3)
¼
x
7
3
6 4x
¼
7 3
18 ¼ 28x
18=28 ¼ x
9=14 ¼ x
(Chapter 10 Lesson 4: Rate Problems)
38. 6/13 or .461 or .462 Since there is a whole
number of crayons in the box, saying that the ratio
of red crayons to blue crayons is 2:3 implies that
the number of red crayons is a multiple of 2 and
the number of blue crayons is a multiple of 3. Likewise, saying that the ratio of blue crayons to yellow
crayons is 2:1 implies that the number of blue
crayons is a multiple of 2 and the number of yellow
crayons is a multiple of 1. So, the number of blue
crayons must be a multiple of both 2 and 3. The smallest such number is 6, so let’s assume that there are 6
blue crayons in the box. Since r:6 ¼ 2:3, there must
be 4 red crayons in the box, and since 6:y ¼ 2:1,
there must be 3 yellow crayons in the box. Therefore,
there are 6 þ 4 þ 3 ¼ 13 crayons in the box, and since
6 of them are blue, the probability of choosing a blue
384
at random is 6/13.
(Chapter 10 Lesson 5: Counting Problems)
(Chapter 10 Lesson 6: Probability Problems)
(Chapter 8 Lesson 4: Ratios and Proportions)
Section 5
1. C
The first phrase of the sentence, which is not
underlined (and therefore cannot be changed), modifies things that are used intelligently. The law of
proximity says that these things should follow the
modifying phrase. The context of the sentence indicates that these things are mnemonics (not you or
facts), and so (C) is the best choice.
(Chapter 13 Lesson 8: Other Misplaced Modifiers)
2. B
The original sentence contains no verb. The
core of the sentence should state that the annual conference . . . was dedicated to . . . resolving disputes.
Choices (B), (D), and (E) make this correction, but
since choices (D) and (E) contain errors in idiom—
dedicated for and dedicated toward instead of dedicated to—the best choice is (B).
(Chapter 13 Lesson 2: Trimming Sentences)
(Chapter 13 Lesson 10: Idiom Errors)
3. E
The original sentence is unnecessarily wordy
and suggests that the doctor was a time, which is illogical. Choice (E) uses 70% fewer words to say everything that the original phrase is trying to say, and
so is much better.
(Chapter 13 Lesson 12: Other Problems with
Modifiers)
4. C
The original “sentence” is not a complete
thought, because it lacks a verb. It is also needlessly
wordy: why say because of the fact that when
because will do? Choice (C) is the most concise, yet
expresses a clear and complete thought.
(Chapter 13 Lesson 12: Other with Modifiers
Problems)
(Chapter 13 Lesson 15: Coordinating Ideas)
5. D
This sentence has the structure A is B, where
A is one aspect of the play. Therefore, B must be a
phrase that is logically and grammatically equivalent
to one aspect of the play. As it stands, B is an independent clause, but should be a noun phrase, because A
is a noun phrase. Choices (D) and (E) are noun
phrases, but choice (E) suggests that the social
issue, rather than the play, is humorous. Therefore,
the best choice is (D).
(Chapter 13 Lesson 15: Coordinating Ideas)
MC GRAW-HILL’S PSAT/NMSQT
6. A
The original phrasing is clear, complete,
logical, and concise.
7. E
The Senator has completed campaigning,
since she is now home with her family. Therefore,
the present participle campaigning is incorrect and
should instead be the present perfect participle:
having campaigned.
(Chapter 13 Lesson 9: Tricky Tenses)
8. C
This sentence contains the parallel phrasing
not so much A as B, and so A and B must have the
same grammatical structure. Since A is the
common noun phrase a suspense thriller, B should
also be a common noun phrase, as in choice (C).
(Chapter 13 Lesson 3: Parallelism)
9. A
The original phrasing is clear, complete,
logical, and concise.
10. E
Since the sentence suggests that Jermaine
was playing at that time, and as if he had played
over an extended time in the past, the tense should
be the past perfect progressive: had been playing.
(Chapter 13 Lesson 9: Tricky Tenses)
11. C
This sentence lists the factors that influence
the price of crude oil, and so the items in this list
should follow the law of parallelism. The first two
items in the list have the form “something in something”: advancements in technology and patterns in
the weather, so the third item should have the same
form: changes in the global political climate. Also,
choice (C) is the most concise of the choices.
(Chapter 13 Lesson 3: Parallelism)
12. B
The Mississippi Pastoral, since it is italicized, must be the title of something. The context of
the sentence makes it clear that it must be one of
the symphonies performed in the festival. This modifying phrase is so far from the word it modifies,
however, that its meaning is unclear. Choice (B)
moves this phrase closer to the word it modifies,
and so is the best choice.
(Chapter 13 Lesson 8: Other Misplaced Modifiers)
13. B
The sentence shows a contrast between a
fact and a misconception. All of the choices indicate
this contrast in some way, but only choice (B) uses
the correct idiom: it originated in China and so did
not originate in Italy.
(Chapter 13 Lesson 5: Pronoun Agreement)
14. C
The sentence indicates that the students do
two things, so these should have parallel phrasing.
CHAPTER 14 / PRACTICE PSAT 1
The course requires that students work and that students discuss.
(Chapter 13 Lesson 3: Parallelism)
15. D
The opening phrase is a participial phrase
that modifies Brice, and not Brice’s stubbornness, so
the original phrase dangles. Choices (C) and (D)
correct the dangling problem, but (D) is the only
one that is phrased logically.
(Chapter 13 Lesson 7: Dangling and Misplaced
Participles)
16. A
The original phrasing is clear, complete,
logical, and concise.
17. C
The original “sentence” does not convey
a complete thought because it does not contain
a verb. Choice (C) corrects this problem most
concisely.
(Chapter 13 Lesson 2: Trimming Sentences)
18. B
The original phrasing is unidiomatic. The
seat belts do not save lives for people, but save the
lives of people. Choice (B) is the most concise yet
idiomatic choice.
(Chapter 13 Lesson 10: Idiom Errors)
19. E
The original phrasing is not parallel. If the
demand increases as the value of the dollar increases,
then it also increases as trade barriers are lowered.
(Chapter 13 Lesson 3: Parallelism)
20. D
As it is originally phrased, the sentence is a
run-on, because two independent clauses are joined
with only a comma. By changing this phrasing to
that in choice (D), the second clause becomes dependent, and this fixes the problem. Choice (C) also
creates a dependent clause, but it is illogical—officials are people, not things.
(Chapter 13 Lesson 15: Coordinating Ideas)
21. B
Since the dumbwaiter is only one thing,
choice (B) should be changed to which has been.
(Chapter 13 Lesson 5: Pronoun Agreement)
22. D Since the closing happened after the rush of
investors, the use of the perfect infinitive to have
closed is illogical. It should be changed to to close.
(Chapter 13 Lesson 9: Tricky Tenses)
23. C
This sentence suggests the parallel phrasing
not only A but also B. This requires changing choice
(C) to but also.
(Chapter 13 Lesson 3: Parallelism)
385
24. D
The subject of the sentence is geometric
design, which is singular. Therefore the verb should
be attests to.
(Chapter 13 Lesson 1: Subject-Verb Disagreement)
25. B The word tactful means sensitive to the needs
of others in delicate social situations, and so is illogical in this context. The correct word here is tactical,
which means pertaining to tactics.
(Chapter 13 Lesson 11: Diction Errors)
26. E
This sentence is correct.
27. A
The phrase usually never is logically contradictory. More logical phrasings that convey the right
idea are hardly ever or almost never.
(Chapter 13 Lesson 12: Other Problems with
Modifiers)
28. B
The correct phrasing is as she (is) because
the pronoun is the subject of an implied verb
(Chapter 18 Lesson 6: Pronoun Case)
29. B
The word should be cleanly, because it is an
adverb modifying the verb burns.
(Chapter 13 Lesson 12: Other Problems with
Modifiers)
30. E
The sentence is correct.
31. B
The subject of the verb is ministers, which is
plural. The correct verb conjugation, then, is have.
(Chapter 13 Lesson 1: Subject-Verb Disagreement)
32. C
This phrase is the antecedent of the
pronoun it, which is singular. Therefore it should
be the fax machine.
(Chapter 13 Lesson 5: Pronoun Agreement)
33. E
The sentence is correct.
34. A
The subject of the verb is two oxygen tanks,
which is plural. The correct phrasing, then, is
there are.
(Chapter 13 Lesson 1: Subject-Verb Disagreement)
35. A
The pronoun they has an ambiguous
antecedent: it could refer to many people or different
fields. Therefore, rephrasing it to these fields clarifies
the sentence.
(Chapter 13 Lesson 5: Pronoun Agreement)
36. B This sentence should be placed between sentence 2 and sentence 3, because sentence 2 describes
one way, and the inserted sentence follows logically
386
with another way. The inserted sentence must also
precede sentence 3, because the inserted sentence
provides only background information to the
central idea of the passage, which is introduced in
sentence 3.
(Chapter 13 Lesson 15: Coordinating Ideas)
37. D
The original phrasing is awkward and
wordy. Choice (D) is far more concise, and is the
clearest of the alternatives because it uses the active
voice, a strong subject, and a concrete subject.
(Chapter 13 Lesson 15: Coordinating Ideas)
38. E
The original phrasing contains two errors in
idiom: used for projecting and projecting on. The
correct idioms are used to project and project onto.
Also, since the sentence discusses many artists and
many images, there must have been many screens.
(Chapter 13 Lesson 10: Idiom Errors)
MC GRAW-HILL’S PSAT/NMSQT
(Chapter 13 Lesson 12: Other Problems with
Modifiers)
39. E
Choice (A) undermines the purpose of the
essay by suggesting that its topic is irrelevant, and
so is a very poor ending. Choice (B) does not
provide a concluding thought, but rather an incidental comment that is only tangentially related to the
rest of the essay. Choice (C) likewise introduces a
thought begging to be developed, rather than a conclusive and hopeful note as the question requires.
Choice (D) seems to provide a conclusive thought
with an air of hope, but it is not appropriate to the
final paragraph, which discusses the controversy
behind Hockney’s theory. Choice (E) fits logically
into such a discussion and also provides a hopeful
concluding thought.
(Chapter 13 Lesson 15: Coordinating Ideas)